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[]
[null,"Excel Business\nStatistical Analysis:"]
[]
[]
[]
[]
[]
[null,"Introduction to Probability"]
[null,"Experiments, Sample Points, Events and then Probability"]
[]
[]
[null,"Excel Business Statistics 16"]
[]
[]
[]
[]
[null,"Excel Statistical Analysis 7: Cross Tabulation, Visualizations, AND Logical Tests, Simpson’s Paradox"]
[null,{"$f":"LEN(B17)","v":100}]
[null,null,{"$f":"LEN(C18)","v":0}]
[]
[]
[]
[null,null,null,null,null,null,null,"Microsoft 365 Excel"]

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[]
[null,"Excel Business\nStatistical Analysis:"]
[]
[]
[]
[]
[]
[null,"Logical Tests for Probability"]
[null,"AND, OR, NOT and the\nCOUNTIFS & FILTER functions!"]
[]
[]
[null,"Excel Business Statistics 17"]
[]
[]
[]
[]
[null,"Excel Statistical Analysis 7: Cross Tabulation, Visualizations, AND Logical Tests, Simpson’s Paradox"]
[null,{"$f":"LEN(B17)","v":100}]
[null,null,{"$f":"LEN(C18)","v":0}]
[]
[]
[]
[null,null,null,null,null,null,null,"Microsoft 365 Excel"]

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[]
[null,"Excel Business\nStatistical Analysis:"]
[]
[]
[]
[]
[]
[null,"Addition Law of Probability:"]
[null,"OR Logical Test"]
[]
[]
[null,"Excel Business Statistics 18"]
[]
[]
[]
[]
[null,"Excel Statistical Analysis 7: Cross Tabulation, Visualizations, AND Logical Tests, Simpson’s Paradox"]
[null,{"$f":"LEN(B17)","v":100}]
[null,null,{"$f":"LEN(C18)","v":0}]
[]
[]
[]
[null,null,null,null,null,null,null,"Microsoft 365 Excel"]

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[]
[null,"Excel Business\nStatistical Analysis:"]
[]
[]
[]
[]
[]
[null,"Conditional Probability"]
[]
[]
[]
[null,"Excel Business Statistics 19"]
[]
[]
[]
[]
[null,"Excel Statistical Analysis 7: Cross Tabulation, Visualizations, AND Logical Tests, Simpson’s Paradox"]
[null,{"$f":"LEN(B17)","v":100}]
[null,null,{"$f":"LEN(C18)","v":0}]
[]
[]
[]
[null,null,null,null,null,null,null,"Microsoft 365 Excel"]

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[]
[null,"Excel Business\nStatistical Analysis:"]
[]
[]
[]
[]
[]
[null,"Joint Probability Table"]
[]
[]
[]
[null,"Excel Business Statistics 20"]
[]
[]
[]
[]
[null,"Excel Statistical Analysis 7: Cross Tabulation, Visualizations, AND Logical Tests, Simpson’s Paradox"]
[null,{"$f":"LEN(B17)","v":100}]
[null,null,{"$f":"LEN(C18)","v":0}]
[]
[]
[]
[null,null,null,null,null,null,null,"Microsoft 365 Excel"]

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[]
[null,"Excel Business\nStatistical Analysis:"]
[]
[]
[]
[]
[]
[null,"Multiplication Law of Probability:"]
[null,"AND Logical Test\n(Probability Tree too)"]
[]
[]
[null,"Excel Business Statistics 21"]
[]
[]
[]
[]
[null,"Excel Statistical Analysis 7: Cross Tabulation, Visualizations, AND Logical Tests, Simpson’s Paradox"]
[null,{"$f":"LEN(B17)","v":100}]
[null,null,{"$f":"LEN(C18)","v":0}]
[]
[]
[]
[null,null,null,null,null,null,null,"Microsoft 365 Excel"]

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[]
[null,"Excel Business\nStatistical Analysis:"]
[]
[]
[]
[]
[]
[null,"Bayes' Theorem"]
[]
[]
[]
[null,"Excel Business Statistics 22"]
[]
[]
[]
[]
[null,"Excel Statistical Analysis 7: Cross Tabulation, Visualizations, AND Logical Tests, Simpson’s Paradox"]
[null,{"$f":"LEN(B17)","v":100}]
[null,null,{"$f":"LEN(C18)","v":0}]
[]
[]
[]
[null,null,null,null,null,null,null,"Microsoft 365 Excel"]

{"sheet":"Topics","index":7,"n_rows":13,"n_cols":3,"rows_kept":13,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Chapter 4"]
[]
[null,"Introduction to Probability"]
[]
[]
[null,"Video 16","Introduction to Probability: Sample Points, Events & Probability"]
[null,"Video 17","Logical Tests for Probability with COUNTIFS and the FILTER functions"]
[null,"Video 18","Adding Law of Probability: OR Logical Test"]
[null,"Video 19","Conditional Probability"]
[null,"Video 20","Joint Probability Table"]
[null,"Video 21","Multiplication Law of Probability: AND Logical Test. Probability Tree too"]
[null,"Video 22","Bayes' Theorem"]

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[]
[null,"Introduction To Probability Chapter 4 Notes by excelisfun"]
[null,"Probability",null,null,null,null,null,null,null,null,null,"Ctrl + P to print all 26 pages of notes : )"]
[null,"Probability = likelihood = chance = possibility"]
[null,"Probability is a numerical measure, a number between 0 and 1 (inclusive), that indicates the likelihood that an event will occur in the unknown future."]
[null,"Probability is never known with certainty. It is only an estimate."]
[null,"Probability is an estimate of an event that may occur in the future."]
[null,"Probability is never negative."]
[null,"Probability is never greater than 1."]
[null,"A percentage change amount is not probability. Remember, you can have an increase in sales of 110% (>1) or a decrease in sales of -25% (<0), but those are NOT probabilities."]
[null,"Probability represents parts out of 100, where you can have 0 to 100 parts out of 100. If the  probability of a sale for any one sales call is 0.20, this means that in a random test you would expect to make 20 sales for every 100 sales calls."]
[null,"Examples:"]
[null,"1) Probability that you will roll a 6 with a die = P(roll six) = 1/6 = 0.1667 = 16.67%"]
[null,"2) Probability that a randomly selected student in my class will earn an A = P(Earn A) = 0.10 = 10%"]
[null,"3) On Jan. 25, 2022, a Casino estimated probability that the KC Chiefs would win super bowl = P(win) = 0.43 =43%"]
[null,"4) On Jan 31, 2022, the probability that the KC Chiefs would win super bowl = P(win) = 0 = 0%"]
[null,"5) The probability that it will rain in Seattle next year = approximately 1 = 100%"]
[]
[null,"Methods for estimating probability:"]
[null,"Classical Probability = All outcomes equally likely.\nExample: probability of rolling a 3 with one die = 1/6 = 0.1666."]
[]
[null,"Relative Frequency Probability = Use past data to create relative frequency distribution.\nExample: probability of getting an A in a class based on past data = 5/50 = 1/10 = 0.10"]
[]
[null,"Subjective Probability = Expert judgement because outcomes are not equally likely and there is little past data. Example: Casino estimates that the probability that KC Chiefs will win Super Bowl = 0.43"]
[null,"Random Experiment"]
[null,"A process that generates well defined Experimental Outcomes (Sample Points)."]
[null,"On any single repetition or trial or step of the experiment, one and only one of the possible experimental outcomes (sample points) can occur."]
[null,"The experimental outcome that occurs on any trial is determined solely by change."]
[null,"Sample Space for a random experiment"]
[null,"A set of all experimental outcomes for a random experiment."]
[null,"It is not always possible to list all experimental outcomes."]
[null,"Examples of 1-step random experiment:"]
[null,"Random Experiment:",null,null,null,"Sample Space:"]
[null,"1) Roll a die",null,null,null,"1,2,3,4,5,6"]
[]
[null,"2) Select a product for inspection",null,null,null,"Defect, Not Defect"]
[]
[null,"3) Play Super Bowl",null,null,null,"Win, Lose"]
[]
[null,"4) Play NFL game",null,null,null,"Win, Lose, Tie"]
[]
[null,"Examples of multi-step random experiment:"]
[null,"Random Experiment:",null,null,null,"Sample Space:"]
[null,"1) Flip coin two times",null,null,null,"(H,H), (H,T), (T,H), (T,T)"]
[]
[null,"2) Roll two die (dice)",null,null,null,{"$f":"_xlfn.TEXTJOIN(\", \",,\"(\"&_xlfn.ANCHORARRAY('Probability Notes'!C125)&\",\"&_xlfn.ANCHORARRAY('Probability Notes'!D124)&\")\")","v":"(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)"}]
[null,"3) 2-step building zoning process",null,null,null,"(Positive Recommendation, Approve), (Positive Recommendation, Disapprove), (Negative Recommendation, Approve), (Negative Recommendation, Disapprove)"]
[]
[null,"Use Tree Diagram to visualize Sample Space and show all experimental outcomes (sample points):"]
[]
[null,"Three Examples for random experiment flipping a coin three times:"]
[]
[null,"1) Worksheet Cells & Formatting:"]
[null,null,null,null,"Step 1","Step 2","Step 3","Sample Space"]
[]
[null,null,null,null,null,null,"Head","(H, H, H)"]
[null,null,null,null,null,"Head"]
[null,null,null,null,null,null,"Tail","(H, H, T)"]
[null,null,null,null,"Head"]
[null,null,null,null,null,null,"Head","(H, T, H)"]
[null,null,null,null,null,"Tail"]
[null,null,null,null,null,null,"Tail","(H, T, T)"]
[null,"Flip a Coin 3 Times."]
[null,null,null,null,null,null,"Head","(T, H, H)"]
[null,null,null,null,null,"Head"]
[null,null,null,null,null,null,"Tail","(T, H, T)"]
[null,null,null,null,"Tail"]
[null,null,null,null,null,null,"Head","(T, T, H)"]
[null,null,null,null,null,"Tail"]
[null,null,null,null,null,null,"Tail","(T, T, T)"]
[null,"2) Excel Smart Art Horizontal Hierarchy :"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"3) Drawing on Paper:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
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[]
[]
[]
[]
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[]
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[]
[null,"Use Table Format to visualize Sample Space and show all experimental outcomes (sample points):"]
[]
[null,"Example of table to visualize all sample points for a two-step random experiment of throwing two die:"]
[]
[null,null,"Die1/Die2",{"$f":"_xlfn.SEQUENCE(,6)","v":1},2,3,4,5,6]
[null,null,{"$f":"_xlfn.SEQUENCE(6)","v":1},{"$f":"\"(\"&_xlfn.ANCHORARRAY(C125)&\",\"&_xlfn.ANCHORARRAY(D124)&\") = \"&_xlfn.ANCHORARRAY(C125)+_xlfn.ANCHORARRAY(D124)","v":"(1,1) = 2"},"(1,2) = 3","(1,3) = 4","(1,4) = 5","(1,5) = 6","(1,6) = 7"]
[null,null,2,"(2,1) = 3","(2,2) = 4","(2,3) = 5","(2,4) = 6","(2,5) = 7","(2,6) = 8"]
[null,null,3,"(3,1) = 4","(3,2) = 5","(3,3) = 6","(3,4) = 7","(3,5) = 8","(3,6) = 9"]
[null,null,4,"(4,1) = 5","(4,2) = 6","(4,3) = 7","(4,4) = 8","(4,5) = 9","(4,6) = 10"]
[null,null,5,"(5,1) = 6","(5,2) = 7","(5,3) = 8","(5,4) = 9","(5,5) = 10","(5,6) = 11"]
[null,null,6,"(6,1) = 7","(6,2) = 8","(6,3) = 9","(6,4) = 10","(6,5) = 11","(6,6) = 12"]
[]
[null,null,{"$f":"_xlfn.IFNA(\"Die 1 formula: \"&_xlfn.FORMULATEXT(C125),\"\")","v":"Die 1 formula: =SEQUENCE(6)"}]
[null,null,{"$f":"_xlfn.IFNA(\"Die 2 formula: \"&_xlfn.FORMULATEXT(D124),\"\")","v":"Die 2 formula: =SEQUENCE(,6)"}]
[null,null,{"$f":"_xlfn.IFNA(\"Inside formula: \"&_xlfn.FORMULATEXT(D125),\"\")","v":"Inside formula: =\"(\"&C125#&\",\"&D124#&\") = \"&C125#+D124#"}]
[]
[null,"Counting Rule for Multi-Step Random Experiment"]
[null,"Total number of experimental outcomes (sample points) = size of sample space = n1 * n2 * … nk"]
[null,"k = Number of steps or trials in the random experiment"]
[null,"n1 = number of possible outcomes in step 1"]
[null,"n2 = number of possible outcomes in step 2"]
[null,"nk = number of possible outcomes in last step"]
[null,"Examples:"]
[null,"1) Roll two die. k = 2, n1 = 6, n2 = 6. Total experiments outcomes = 6*6 = 36",null,null,null,null,null,null,null,null,null,"Flip coin two times. k = 2, n1 = 2, n2 = 2. Total experiments outcomes = 2*2 = 4"]
[]
[null,"2) Determine lock code with 3 spots and 10 digits. What are the number of total experimental outcomes (total possible lock codes)?"]
[]
[null,"Number slots for lock code:",null,null,"k",3]
[null,{"$f":"\"Digits: \"&_xlfn.TEXTJOIN(\", \",,_xlfn.SEQUENCE(,10))","v":"Digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10"},null,null,"n1",10]
[null,{"$f":"\"Digits: \"&_xlfn.TEXTJOIN(\", \",,_xlfn.SEQUENCE(,10))","v":"Digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10"},null,null,"n2",10]
[null,{"$f":"\"Digits: \"&_xlfn.TEXTJOIN(\", \",,_xlfn.SEQUENCE(,10))","v":"Digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10"},null,null,"n3",10]
[null,null,"Total lock possibilities:",null,null,{"$f":"F148*F149*F150","v":1000},{"$f":"_xlfn.IFNA(\" \"&F148&\"*\"&F149&\"*\"&F150&\" or \"&F148&\"^\"&F147,\"\")","v":" 10*10*10 or 10^3"}]
[]
[null,"3) Deli offers 2 rolls, 4 meats and 3 cheeses. k = 3, n1 = 2, n2 = 4, n3 = 3. What are the number of total experimental outcomes (total number of different sandwiches) if you get one of each?"]
[]
[null,"# steps in building sandwich:",null,null,"k",3]
[null,"Number rolls",null,null,"n1",2]
[null,"Number meats",null,null,"n2",4]
[null,null,null,null,"n3",3]
[null,null,"Total lock possibilities:",null,null,{"$f":"F156*F157*F158","v":24},{"$f":"_xlfn.IFNA(\" \"&F156&\"*\"&F157&\"*\"&F158,\"\")","v":" 2*4*3"}]
[]
[]
[null,"Sometimes we have to decide on sample space with combinations or permutations, where you select n objects from a set of N objects."]
[]
[null,"Example of the difference between a Combination and a Permutation:"]
[null,"If we select the letters A, B, C, one after the other and you cannot repeat (example: A, A, A not allowed)"]
[]
[null,null,"Permutations",null,"Combinations"]
[null,null,"Order Matters",null,"Order Does Not Matter",null,"* You can pick the letters in any"]
[null,null,"A, B, C",null,"A, B, C",null,"order, but just one time."]
[null,null,"A, C, B"]
[null,null,"B, A, C"]
[null,null,"B, C, A"]
[null,null,"C, A, B"]
[null,null,"C, B, C"]
[null,"Total",{"$f":"COUNTA(C169:C174)","v":6},null,{"$f":"COUNTA(E169:E174)","v":1}]
[]
[]
[null,"Counting Rule for Combinations, Order Does Not Matter"]
[null,"When experiment involves selecting n objects from a set of N objects, and the order of the items is not considered, like: (2,1) is the same as (1,2), then:\nTotal number of experimental outcomes (sample points) = size of sample space ="]
[]
[]
[]
[null,"N = count of all objects (population)",null,null,null,null,7,"Population Size"]
[null,"n = count of  objects selected (sample size)",null,null,null,null,3,"Sample Size"]
[null,"In Excel use function: COMBIN(N,n)",null,null,null,null,{"$f":"COMBIN(G183,G184)","v":35},"Total combinations"]
[null,null,null,null,null,null,{"$f":"_xlfn.IFNA(\"=COMBIN(\"&G183&\",\"&G184&\")\",\"\")","v":"=COMBIN(7,3)"}]
[null,"Note: Factorial (from your algebra class) is represented by ! Example: 5! = 5*4*3*2*1 = 120, and: 0! = 1."]
[null,"Examples:"]
[null,"1) Find all possible combinations of sample size 3 from a set of 7 numbers = 7!/(3!*(7-3)!) = (7*6*5*4*3*2*1)/(3*2*1*(4*3*2*1)) = (7*6*5)/(3*2*1*) = 7*5 = 35"]
[]
[null,"2) Find all combinations a for a basketball team that has 13 players and 5 can play in a game, assuming a player can play any position = 13!/(5!*(13-5) = (13*12*11*10*9)/(5*4*3*2*1) =\n(13*3*11*2*3)/2 = 1287"]
[]
[null,"Counting Rule for Permutations, Order Matters"]
[null,"When experiment involves selecting n objects from a set of N objects, and the order of the items is considered, like: (2,1) is different than (1,2), then:\nTotal number of experimental outcomes (sample points) = size of sample space = "]
[null,null,null,null,null,null,null,null,null,null,null,null,"Good site for other types of combinations and permutations, and for a description of why these formulas are valid:"]
[null,null,null,null,null,null,null,null,null,null,null,null,"https://www.mathsisfun.com/combinatorics/combinations-permutations.html"]
[]
[null,"N = count of all objects (population)",null,null,null,null,5,"Population Size"]
[null,"n = count of  objects selected (sample size)",null,null,null,null,5,"Sample Size"]
[null,"In Excel use function: PERMUT(N,n)",null,null,null,null,{"$f":"PERMUT(G198,G199)","v":120},"Total permutations"]
[null,null,null,null,null,null,{"$f":"_xlfn.IFNA(\"=PERMUT(\"&G198&\",\"&G199&\")\",\"\")","v":"=PERMUT(5,5)"}]
[null,"Examples:"]
[null,"1) Find total possible arrangements for 5 employees in 5 different offices = 5!/(5-5)! = (5*4*3*2*1)/0! = 120/1 = 120"]
[null,"2) Find total possible arrangements for 5 employees in 3 different offices = 5!/(5-3)! = (5*4*3*2*1)/2! = 120/2 = 60"]
[]
[null,{"$f":"M195&\"   \"&M196","v":"Good site for other types of combinations and permutations, and for a description of why these formulas are valid:   https://www.mathsisfun.com/combinatorics/combinations-permutations.html"}]
[]
[null,"Basic Requirements for Assigning Probabilities"]
[null,"1] The probability for each experimental outcome (sample point) must be between 0 and 1, inclusive."]
[null,"0 <= P(Ei) <= 1 for all i,   where: Ei = ith experimental outcome and P(Ei) = Probability."]
[]
[null,"2] The sum of the probabilities for all experimental outcomes (sample points) from the sample space must be equal to 1."]
[null,"P(E1) +  P(E2) + … +  P(En) = 1,  where there are n experimental outcomes."]
[]
[null,"Event"]
[null,"A collection of  one or more experimental outcomes (sample points)."]
[null,"Examples:"]
[null,"1) The event roll a 7 with dice has the following sample points: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)."]
[]
[null,"2) The event get one or more tails in two flips of a coin has the following sample points:\n(T,T), (H,T), (T,H)"]
[]
[null,"3) The event sold a Quad from a list of products sold: Quad,Carlota,Quad,Sunshine, has the following sample points: (Quad,Quad)."]
[]
[null,"Note: Sample points and events provide the foundation for the study of probability."]
[null,"Probability of an Event"]
[null,"The probability of an event is equal to the sum of the probabilities of the experimental outcomes (sample points) in the event."]
[]
[null,"Examples:"]
[null,"1) Event = Roll a 7 with dice"]
[null,"Sample points = (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)"]
[null,"Probability = P(Roll 7) = 1/36+1/36+1/36+1/36+1/36+1/36 = 6/36 = 1/6 = 0.1667"]
[]
[null,"All sample points for experiment \"roll dice\":"]
[]
[null,null,"Die1/Die2",{"$f":"_xlfn.SEQUENCE(,6)","v":1},2,3,4,5,6]
[null,null,{"$f":"_xlfn.SEQUENCE(6)","v":1},{"$f":"\"(\"&_xlfn.ANCHORARRAY(C236)&\",\"&_xlfn.ANCHORARRAY(D235)&\") = \"&_xlfn.ANCHORARRAY(C236)+_xlfn.ANCHORARRAY(D235)","v":"(1,1) = 2"},"(1,2) = 3","(1,3) = 4","(1,4) = 5","(1,5) = 6","(1,6) = 7"]
[null,null,2,"(2,1) = 3","(2,2) = 4","(2,3) = 5","(2,4) = 6","(2,5) = 7","(2,6) = 8"]
[null,null,3,"(3,1) = 4","(3,2) = 5","(3,3) = 6","(3,4) = 7","(3,5) = 8","(3,6) = 9"]
[null,null,4,"(4,1) = 5","(4,2) = 6","(4,3) = 7","(4,4) = 8","(4,5) = 9","(4,6) = 10"]
[null,null,5,"(5,1) = 6","(5,2) = 7","(5,3) = 8","(5,4) = 9","(5,5) = 10","(5,6) = 11"]
[null,null,6,"(6,1) = 7","(6,2) = 8","(6,3) = 9","(6,4) = 10","(6,5) = 11","(6,6) = 12"]
[]
[null,"All probabilities for experiment \"roll dice\":"]
[]
[null,null,"Die1/Die2",{"$f":"_xlfn.SEQUENCE(,6)","v":1},2,3,4,5,6]
[null,null,{"$f":"_xlfn.SEQUENCE(6)","v":1},{"$f":"_xlfn.SEQUENCE(6,6,1,0)&\"/\"&6^2","v":"1/36"},"1/36","1/36","1/36","1/36","1/36"]
[null,null,2,"1/36","1/36","1/36","1/36","1/36","1/36"]
[null,null,3,"1/36","1/36","1/36","1/36","1/36","1/36"]
[null,null,4,"1/36","1/36","1/36","1/36","1/36","1/36"]
[null,null,5,"1/36","1/36","1/36","1/36","1/36","1/36"]
[null,null,6,"1/36","1/36","1/36","1/36","1/36","1/36"]
[null,null,null,null,null,null,null,"Total",{"$f":"36/36","v":1}]
[null,"Probability Requirement #1 is met: each 1/36 probability is between 0 and 1."]
[null,"Probability Requirement #2 is met: sum of all probability equals 1: 1/36*36 = 1."]
[]
[null,"2) Event = Get 2 tails in three flips of a coin"]
[null,{"$f":"\"Sample points = \"&_xlfn.TEXTJOIN(\", \",,F267:F269)","v":"Sample points = (H, T, T), (T, H, T), (T, T, H)"}]
[null,"Probability = P(2T in 3 Tries) = 1/8+1/8+1/8 = 3/8 = 0.375"]
[]
[null,"All probabilities for experiment \"flip fair coin three times\":"]
[]
[null,null,"Step 1","Step 2","Step 3","Sample Space","P(SP)"]
[null,null,"H","H","H",{"$f":"\"(\"&C263:C270&\", \"&D263:D270&\", \"&E263:E270&\")\"","v":"(H, H, H)"},{"$f":"_xlfn.SEQUENCE(8,,1,0)&\"/\"&8","v":"1/8"}]
[null,null,"H","H","T","(H, H, T)","1/8"]
[null,null,"H","T","H","(H, T, H)","1/8"]
[null,null,"T","H","H","(T, H, H)","1/8"]
[null,null,"H","T","T","(H, T, T)","1/8"]
[null,null,"T","H","T","(T, H, T)","1/8"]
[null,null,"T","T","H","(T, T, H)","1/8"]
[null,null,"T","T","T","(T, T, T)","1/8"]
[null,null,null,null,null,"Total",{"$f":"8/8","v":1}]
[]
[null,"Probability Requirement #1 is met: each 1/8 probability is between 0 and 1."]
[null,"Probability Requirement #2 is met: sum of all probability equals 1: 1/8*8 = 1."]
[]
[null,"3) Event = Use 2 or more banquet rooms at Isaac's Italian Restaurant on a weekend day."]
[null,"\"Sample points\" from pre-made frequency distribution = 2 rooms used, 3 rooms used, 4 rooms used."]
[null,{"$f":"\"Probability = P(Rooms Used>=2) = \"&ROUND(I285,2)&\" + \"&ROUND(I286,2)&\" = \"&ROUND(I287,2)&\" = \"&ROUND(SUM(I285:I287),2)&\", or, (\"&H285&\" + \"&H286&\" + \"&H287&\")/\"&H288&\" = \"&SUM(H285:H287)&\"/\"&H288&\" = \"&ROUND(SUM(H285:H287)/H288,2)","v":"Probability = P(Rooms Used>=2) = 0.43 + 0.27 = 0.08 = 0.78, or, (45 + 28 + 8)/104 = 81/104 = 0.78"}]
[]
[null,"Summary of all 104 sample points & probabilities into a frequency distribution:"]
[]
[null,null,null,null,null,null,"# Rooms Used in Day (x)","Frequency","% Frequency or P(x)"]
[null,null,null,null,null,null,0,2,1.9230769230769232E-2]
[null,null,null,null,null,null,1,21,0.20192307692307693]
[null,null,null,null,null,{"$f":"H285:H287&\" sample points @ 1/\"&H288&\" probability each \"&_xlfn.UNICHAR(10142)","v":"45 sample points @ 1/104 probability each ➞"},2,45,0.43269230769230771]
[null,null,null,null,null,"28 sample points @ 1/104 probability each ➞",3,28,0.26923076923076922]
[null,null,null,null,null,"8 sample points @ 1/104 probability each ➞",4,8,7.6923076923076927E-2]
[null,null,null,null,null,null,"Total",104,1]
[null,"Probability Requirement #1 is met: each probability is between 0 and 1."]
[null,{"$f":"\"Probability Requirement #2 is met: sum of all probability equals 1: \"&_xlfn.TEXTJOIN(\"+\",,TEXT(I283:I287,\"0%\"))&\" = \"&I288","v":"Probability Requirement #2 is met: sum of all probability equals 1: 2%+20%+43%+27%+8% = 1"}]
[]
[]
[null,"Venn Diagram",null,null,null,null,"Name","Hair Color","Eye Color"]
[null,"Diagram to show relationship between different events",null,null,null,null,"Sioux","Brown","Hazel"]
[null,"and the sample space for an experiment.",null,null,null,null,"Chin","Black","Blue"]
[null,"Rectangle = sample space = all sample points possible.",null,null,null,null,"Shelia","Black","Brown"]
[null,"Circle = Event (one or more sample points).",null,null,null,null,"Gigi","Brown","Hazel"]
[null,null,null,null,null,null,"Tyrone","Black","Brown"]
[null,"Event Black Hair",null,null,null,null,"Lin","Blond","Brown"]
[null,null,null,null,null,null,"Ducky","Brown","Brown"]
[null,null,null,null,null,null,"Kip","Brown","Hazel"]
[null,null,null,null,null,null,"Linda","Red","Blue"]
[null,null,null,null,null,null,"Jo","Pink","Green"]
[null,null,null,null,null,null,"Total Records:",null,{"$f":"ROWS(G294:I303)","v":10}]
[]
[null,"Event Brown Hair",null,null,null,"Event NOT Brown Hair"]
[]
[]
[]
[]
[]
[]
[]
[null,"Event Brown Hair OR Black Hair",null,null,null,"Complement Rule"]
[null,null,null,null,null,"Given an Event A, the complement of A contains"]
[null,null,null,null,null,"all sample points that are NOT in A."]
[]
[null,null,null,null,null,"Mutually Exclusive Events"]
[null,null,null,null,null,"The two events have no sample points in common."]
[null,null,null,null,null,"No intersection. Not overlap."]
[null,null,null,null,null,"If one mutually exclusive event is known to occur, the"]
[null,"Event Brown Hair OR Hazel Eyes",null,null,null,"other event cannot occur and its probability is reduced to 0."]
[]
[null,null,null,null,null,"Union of Two Events, OR Logical Test"]
[null,null,null,null,null,"The union of A and B is the event that contains"]
[null,null,null,null,null,"all sample points belonging to A or B or both."]
[null,null,null,null,null,"If you are counting, you must subtract"]
[null,null,null,null,null,"the AND section to avoid double counting."]
[null,null,"AND"]
[null,"Event Brown Hair AND Hazel Eyes",null,null,null,"Intersection of Two Events, AND Logical Test"]
[null,null,null,null,null,"The intersection of A and B is the event that"]
[null,null,null,null,null,"contains sample points that belonging"]
[null,null,null,null,null,"to both A and B. There is overlap."]
[null,null,null,null,null,"If you are counting, you only count what is in the AND section."]
[]
[]
[null,null,"AND"]
[]
[]
[null,"Logical Tests Used for Counting Sample Points",null,null,null,null,"Name","HairColor","EyeColor"]
[null,null,null,null,null,null,"Sioux","Brown","Hazel"]
[null,"Event Black Hair",null,null,null,null,"Chin","Black","Blue"]
[null,null,null,null,null,null,"Shelia","Black","Brown"]
[null,null,null,null,null,null,"Gigi","Brown","Hazel"]
[null,null,null,null,null,null,"Tyrone","Black","Brown"]
[null,null,null,null,null,null,"Lin","Blond","Brown"]
[null,null,null,null,null,null,"Ducky","Brown","Brown"]
[null,null,null,null,null,null,"Kip","Brown","Hazel"]
[null,"Event Brown Hair",null,null,null,null,"Linda","Red","Blue"]
[null,null,null,null,null,null,"Jo","Pink","Green"]
[null,null,null,null,null,null,"Total Records:",null,{"$f":"ROWS(G341:I350)","v":10}]
[]
[null,null,null,null,null,"1) Single Condition Logical Test: Equal to Brown Hair"]
[null,null,null,null,null,"Condition","Brown"]
[null,null,null,null,null,"Count",{"$f":"COUNTIFS(HairColor,G354)","v":4},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G355),\"\")","v":"=COUNTIFS(HairColor,G354)"}]
[]
[null,"Event NOT Brown Hair",null,null,null,"P(Brown)",{"$f":"G355/I351","v":0.4}]
[null,null,null,null,null,"2) Not Logical Test: NOT Brown Hair"]
[null,null,null,null,null,"Condition","Brown"]
[null,null,null,null,null,"Count",{"$f":"COUNTIFS(HairColor,\"<>\"&G359)","v":6},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G360),\"\")","v":"=COUNTIFS(HairColor,\"<>\"&G359)"}]
[]
[null,null,null,null,null,"P(Brown)",{"$f":"G360/I351","v":0.6}]
[null,null,null,null,null,"Complement Rule: If P(B), then P(Not B) = 1 - P(B)"]
[null,null,null,null,null,"P(Brown)",{"$f":"1-G357","v":0.6},{"$f":"_xlfn.IFNA(\" 1-\"&G357,\"\")","v":" 1-0.4"}]
[null,"Event Brown Hair OR Black Hair"]
[null,null,null,null,null,"3a) OR Logical Test for Mutually Exclusive Events (One Column):"]
[null,null,null,null,null,"Brown Hair OR Black Hair"]
[null,null,null,null,null,"Condition","Brown",null,null,null,null,"Name","Hair Color","Eye Color"]
[null,null,null,null,null,"Condition","Black",null,null,null,null,"Sioux","Brown","Hazel"]
[null,null,null,null,null,"Count",{"$f":"ROWS(_xlfn._xlws.FILTER(HairColor,(HairColor=G368)+(HairColor=G369)))","v":7},null,null,null,null,"Chin","Black","Blue"]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G370),\"\")","v":"=ROWS(FILTER(HairColor,(HairColor=G368)+(HairColor=G369)))"},null,null,null,null,null,"Shelia","Black","Brown"]
[null,null,null,null,null,"Count",{"$f":"COUNTIFS(HairColor,G368)+COUNTIFS(HairColor,G369)","v":7},null,null,null,null,"Gigi","Brown","Hazel"]
[null,"Event Brown Hair OR Hazel Eyes",null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G372),\"\")","v":"=COUNTIFS(HairColor,G368)+COUNTIFS(HairColor,G369)"},null,null,null,null,null,"Tyrone","Black","Brown"]
[null,null,null,null,null,null,null,null,null,null,null,"Lin","Blond","Brown"]
[null,null,null,null,null,"3b) OR Logical Test for Events that are not Mutually Exclusive",null,null,null,null,null,"Ducky","Brown","Brown"]
[null,null,null,null,null,"Brown Hair OR Hazel Eyes",null,null,"(Two Columns):",null,null,"Kip","Brown","Hazel"]
[null,null,null,null,null,"Condition","Brown","Hair",null,null,null,"Linda","Red","Blue"]
[null,null,null,null,null,"Condition","Hazel","Eyes",null,null,null,"Jo","Pink","Green"]
[null,null,null,null,null,"Count",{"$f":"ROWS(_xlfn._xlws.FILTER(H341:I350,(HairColor=G377)+(EyeColor=G378)))","v":4},null,null,null,null,"Total Records:",null,{"$f":"ROWS(L369:N378)","v":10}]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G379),\"\")","v":"=ROWS(FILTER(H341:I350,(HairColor=G377)+(EyeColor=G378)))"}]
[null,"Event Brown Hair AND Hazel Eyes",null,null,null,"Count",{"$f":"COUNTIFS(HairColor,G377)+COUNTIFS(EyeColor,G378)-COUNTIFS(HairColor,G377,EyeColor,G378)","v":4}]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G381),\"\")","v":"=COUNTIFS(HairColor,G377)+COUNTIFS(EyeColor,G378)-COUNTIFS(HairColor,G377,EyeColor,G378)"}]
[null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G384),\"\")","v":""}]
[null,null,null,null,null,"4) AND Logical Test: Brown Hair AND Hazel Eyes"]
[null,null,null,null,null,"Condition","Brown","Hair"]
[null,null,null,null,null,"Condition","Hazel","Eyes"]
[null,null,null,null,null,"Count",{"$f":"COUNTIFS(HairColor,G385,EyeColor,G386)","v":3}]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G387),\"\")","v":"=COUNTIFS(HairColor,G385,EyeColor,G386)"}]
[]
[]
[null,"Logical Tests Used for Filtering Sample Points",null,null,null,null,"Name","HairColor","EyeColor"]
[null,"We can use the FILTER array function to filter a data set",null,null,null,null,"Sioux","Brown","Hazel"]
[null,"in order to see specified sample points.",null,null,null,null,"Chin","Black","Blue"]
[null,null,null,null,null,null,"Shelia","Black","Brown"]
[null,"FILTER(ArrayToFilter,LogicalTestArray)",null,null,null,null,"Gigi","Brown","Hazel"]
[null,"ArrayToFilter & LogicalTestArray must be same size.",null,null,null,null,"Tyrone","Black","Brown"]
[null,"OR Logical Test uses + in direct array operation.",null,null,null,null,"Lin","Blond","Brown"]
[null,"AND Logical Test uses * in direct array operation.",null,null,null,null,"Ducky","Brown","Brown"]
[null,"TRUE = TRUE or any non-zero number.",null,null,null,null,"Kip","Brown","Hazel"]
[null,"FALSE = FALSE or 0.",null,null,null,null,"Linda","Red","Blue"]
[null,null,null,null,null,null,"Jo","Pink","Green"]
[null,null,null,null,null,null,"Total Records:",null,{"$f":"ROWS(G392:I401)","v":10}]
[null,"Event Brown Hair"]
[null,null,null,null,null,"1) Single Condition Logical Test: Equal to Brown Hair"]
[null,null,null,null,null,"Condition","Brown","Matching Rows:"]
[null,null,null,null,null,null,null,null,{"$f":"_xlfn._xlws.FILTER(HairColor,HairColor=G405)","v":"Brown"}]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(I406),\"\")","v":"=FILTER(HairColor,HairColor=G405)"},null,null,"Brown"]
[null,null,null,null,null,null,null,null,"Brown"]
[null,null,null,null,null,null,null,null,"Brown"]
[]
[null,"Event Brown Hair OR Black Hair",null,null,null,"3a) OR Logical Test for Mutually Exclusive Events (One Column):"]
[null,null,null,null,null,"Brown Hair OR Black Hair"]
[null,null,null,null,null,"Condition","Brown","Matching Rows:"]
[null,null,null,null,null,"Condition","Black",null,{"$f":"_xlfn._xlws.FILTER(HairColor,(HairColor=G413)+(HairColor=G414))","v":"Brown"}]
[null,null,null,null,null,null,null,null,"Black"]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(I414),\"\")","v":"=FILTER(HairColor,(HairColor=G413)+(HairColor=G414))"},null,null,"Black"]
[null,null,null,null,null,null,null,null,"Brown"]
[null,null,null,null,null,null,null,null,"Black"]
[null,"Event Brown Hair OR Hazel Eyes",null,null,null,null,null,null,"Brown"]
[null,null,null,null,null,null,null,null,"Brown"]
[]
[null,null,null,null,null,"3b) OR Logical Test for Events that are not Mutually Exclusive"]
[null,null,null,null,null,null,null,null,"(Two Columns):"]
[null,null,null,null,null,"Brown Hair OR Hazel Eyes"]
[null,null,null,null,null,"Condition","Brown","Hair","Matching Rows:"]
[null,null,null,null,null,"Condition","Hazel","Eyes",{"$f":"_xlfn._xlws.FILTER(H392:I401,(HairColor=G425)+(EyeColor=G426))","v":"Brown"},"Hazel"]
[null,null,null,null,null,null,null,null,"Brown","Hazel"]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(I426),\"\")","v":"=FILTER(H392:I401,(HairColor=G425)+(EyeColor=G426))"},null,null,"Brown","Brown"]
[null,null,null,null,null,null,null,null,"Brown","Hazel"]
[]
[null,null,null,null,null,"4) AND Logical Test: Brown Hair AND Hazel Eyes"]
[null,"Event Brown Hair AND Hazel Eyes",null,null,null,"Condition","Brown","Hair","Matching Rows:"]
[null,null,null,null,null,"Condition","Hazel","Eyes",{"$f":"_xlfn._xlws.FILTER(H392:I401,(HairColor=G432)*(EyeColor=G433))","v":"Brown"},"Hazel"]
[null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G436),\"\")","v":""},null,null,null,"Brown","Hazel"]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(I433),\"\")","v":"=FILTER(H392:I401,(HairColor=G432)*(EyeColor=G433))"},null,null,"Brown","Hazel"]
[]
[]
[]
[]
[]
[null,"FILTER Function"]
[null,"The FILTER array function allows you to filter a set of values to show only that values that meet a logical test. The array argument contains the values that you want to filter. The include argument requires an array of TRUE and FALSE values (same dimension as array argument values) to indicate which values to keep (TRUE) and with ones to filter out (FALSE).\n\nFor an OR Logical Test, use addition,  + operation, like: =FILTER(H54:I63,(H54:H63=G87)+(I54:I63=G88))\n\nFor an AND Logical Test, use multiplication, * operator, like: =FILTER(H54:I63,(H54:H63=G87)*(I54:I63=G88))"]
[null,"COUNTIFS function"]
[null,"The COUNTIFS function makes a conditional count calculation based on one or more logical tests. The criteria_range argument contains the full range with all the conditional items. The criteria argument contains the conditions for counting items from the criteria_range1 argument.\n\nIf you use a single condition like with: =COUNTIFS(H3:H12,G16), you are performing a Single Condition Logical Test.\n\nIf you use two or more conditions like with: =COUNTIFS(M31:M40,G47,N31:N40,G48), you are performing an AND Logical Test.\n\nIf you need to use a comparative operator with the condition, you must join the comparative operator to the cell with the condition, like: \"<>\"&G21. Example for this formula counts items that are not whatever the value in cell G21 is.\n\nYou can have up to 127 pairs of criteria_rangeN criteriaN arguments that will run an AND Logical Test to make the conditional count calculation."]
[null,"Comparative Operator Note:"]
[null,"* When using comparative operators in functions like COUNTIFS, SUMIFS, AVERAGEIFS, MINIFS and MAXIFS, you must join the comparative operator to the cell with the condition, like: \">\"&J28.\n* But when you use a comparative operator in a formula that makes a direct logical test formula calculation, you do not use quotes or an ampersand (join operator), like: H54:H63=G87."]
[]
[null,"More Notes for Important Terms:"]
[null,"Complement Rule"]
[null,"Sample Space = All Sample Points. P(Sample Space) = P(S) = 1."]
[null,"Given an Event A, the complement of A contains all sample points that are NOT in A"]
[null,"If the complement of A = Ac , then P(Ac) = 1 - P(A), or, P(Not A) = 1 - P(A)"]
[null,"Mutually Exclusive"]
[null,"Think of it as \"Dating only one person\"."]
[null,"Two events are said to be mutually exclusive if they have no sample points in common. The intersection of the two events must contain no sample points."]
[null,"Categories in a frequency distribution are mutually exclusive when each item in the sample space can fit into only one category."]
[null,"Events A and B are mutually exclusive if, when one event occurs, the other cannot occur. If one mutually exclusive event is known to occur, the other event cannot occur and its probability is reduced to zero."]
[null,"Two mutually exclusive events are dependent because if one event occurs, the other cannot occur."]
[null,"Union of Two Events, OR Logical Test"]
[null,"The union of A and B is the event that contains all sample points belonging to A or B or both."]
[null,"Notation for Probability is: P(A U B) = P(A OR B), where U = Union / OR."]
[null,"Synonyms: OR = Union = \"At least 1\", \"1 or more\""]
[null,"Intersection of Two Events, AND Logical Test"]
[null,"The intersection of A and B is the event that contains sample points that belonging to both A and B."]
[null,"Notation for Probability is: P(A ∩ B) = P(A AND B), where  ∩  = Intersection / AND."]
[null,"Synonyms: AND = Intersection = Concurrent = Joint = Both."]
[null,"OR Logical Test"]
[null,"An OR Logical Test runs two or more logical test, and requires one or more of the tests to evaluate to TRUE in order for the OR logical Test to deliver a TRUE."]
[null,"For two logical tests: TRUE,TRUE = TRUE; TRUE,FALSE = TRUE; FALSE,TRUE = TRUE; FALSE,FALSE = FALSE."]
[null,"When running an OR Logical Test you use the math operation: addition."]
[null,"When running an OR Logical Test over a single column, the events are mutually exclusive, and therefore you do NOT need to take into account the possibility of double counting."]
[null,"When running an OR Logical Test over two or more columns, the events are not necessarily mutually exclusive, and therefore you must take into account the possibility of double counting."]
[null,"AND Logical Test"]
[null,"An AND Logical Test runs two or more logical test, and requires all tests to evaluate to TRUE in order for the AND logical Test to deliver a TRUE."]
[null,"For two logical tests: TRUE,TRUE = TRUE; TRUE,FALSE = FALSE; FALSE,TRUE = FALSE; FALSE,FALSE = FALSE."]
[null,"When running an AND Logical Test you use the math operation: multiplication."]
[null,"Addition Law of Probability (OR Logical Test / +)"]
[null,"Addition Law is used to calculate the probability of the union of events (probability of an OR Logical Test)."]
[null,"For Mutually Exclusive Events:",null,null,null,null,"Textbook notation:"]
[null,"P(A OR B) = P(A) + P(B)",null,null,null,null,"P(A U B) = P(A) + P(B)"]
[null,"For Events that are NOT Mutually Exclusive:"]
[null,"P(A OR B) = P(A) + P(B) - P(A AND B)",null,null,null,null,"P(A U B) = P(A) + P(B) - P(A ∩ B)"]
[]
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[null,"Using the Addition Law of Probability"]
[null,"Mutually Exclusive Events: P(A OR B) = P(A) + P(B)."]
[null,"Events that are NOT Mutually Exclusive: P(A OR B) = P(A) + P(B) - P(A AND B)."]
[null,null,null,null,null,null,null,null,"SN","PPM"]
[null,"4 examples of calculating the probability for an OR Logical Test:",null,null,null,null,null,null,"Space","Pike's"]
[null,"1) From Data Set",null,null,null,null,null,"Visitor","Needle","Place Market"]
[null,"2) From Frequency Distribution",null,null,null,null,null,1,"Yes","Yes"]
[null,"3) From Cross Tabulated Report",null,null,null,null,null,2,"No","Yes"]
[null,"4) From Pre-determined Probabilities",null,null,null,null,null,3,"No","Yes"]
[null,null,null,null,null,null,null,4,"No","No"]
[null,"1) From Data Set for visitors to Seattle",null,null,null,null,null,5,"Yes","Yes"]
[null,"For a randomly selected Seattle visitor calculate the probability",null,null,null,null,null,6,"Yes","Yes"]
[null,"that they visited the SN or PPM.",null,null,null,null,null,7,"No","No"]
[null,null,"Condition","Yes","from Space Needle field",null,null,8,"Yes","No"]
[null,null,"Count",{"$f":"COUNTIFS(SN,D571)","v":5},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D572),\"\")","v":"=COUNTIFS(SN,D571)"},null,null,9,"No","Yes"]
[null,null,"Condition","Yes","from Pike's Place field",null,null,10,"Yes","Yes"]
[null,null,"Count",{"$f":"COUNTIFS(PPM,D573)","v":7},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D574),\"\")","v":"=COUNTIFS(PPM,D573)"},null,null,"Total Records",null,{"$f":"ROWS(PPM)","v":10}]
[null,null,"Condition","Yes","Visited both sites (AND)"]
[null,null,"Count",{"$f":"COUNTIFS(SN,D575,PPM,D575)","v":4},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D576),\"\")","v":"=COUNTIFS(SN,D575,PPM,D575)"}]
[null,"P(SN OR PPM)",null,{"$f":"(D572+D574-D576)/J574","v":0.8},{"$f":"_xlfn.IFNA(\" (\"&D572&\"+\"&D574&\"-\"&D576&\")/\"&J574,\"\")","v":" (5+7-4)/10"}]
[null,"P(SN OR PPM)",null,{"$f":"ROWS(_xlfn._xlws.FILTER(I564:J573,(SN=D575)+(PPM=D575)))/J574","v":0.8},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D578),\"\")","v":"=ROWS(FILTER(I564:J573,(SN=D575)+(PPM=D575)))/J574"}]
[]
[null,"2) From Frequency Distribution with Mutually Exclusive Categories",null,null,null,null,null,null,"Arrival","Frequency"]
[null,"For a randomly selected Delta Airline Passenger calculate the",null,null,null,null,null,null,"Early",100]
[null,"following probabilities:",null,null,null,null,null,null,"On Time",794]
[null,"P(Early OR On Time)",null,{"$f":"(J581+J582)/J585","v":0.89400000000000002},{"$f":"_xlfn.IFNA(\" (\"&J581&\"+\"&J582&\")/\"&J585,\"\")","v":" (100+794)/1000"},null,null,null,"Late",81]
[null,"P(Cancelled)",null,{"$f":"J584/J585","v":2.5000000000000001E-2},{"$f":"_xlfn.IFNA(\" \"&J584&\"/\"&J585,\"\")","v":" 25/1000"},null,null,null,"Canceled",25]
[null,"P(Not Cancelled)",null,{"$f":"1-D584","v":0.97499999999999998},{"$f":"_xlfn.IFNA(\" 1-\"&D584,\"\")","v":" 1-0.025"},null,null,null,"Grand Total",1000]
[]
[null,"3) From Cross Tabulated Report created from the visitors to Seattle data set "]
[null,"For a randomly selected Seattle visitor calculate the probability"]
[null,"that they visited the SN or PPM.",null,null,null,null,"Frequency","Pike's Place M."]
[null,null,null,null,null,null,"Space N.",{"$f":"TRANSPOSE(_xlfn._xlws.SORT(_xlfn.UNIQUE(J564:J573)))","v":"No"},"Yes","Totals"]
[null,"P(SN OR PPM)",null,{"$f":"(J592+I593-I592)/J593","v":0.8},null,null,{"$f":"_xlfn._xlws.SORT(_xlfn.UNIQUE(I564:I573))","v":"No"},{"$f":"COUNTIFS(I564:I573,G591:G592,J564:J573,H590:I590)","v":2},3,{"$f":"SUM(H591:I591)","v":5}]
[null,null,null,{"$f":"_xlfn.IFNA(\" (\"&J592&\"+\"&I593&\"-\"&I592&\")/\"&J593,\"\")","v":" (5+7-4)/10"},null,null,"Yes",1,4,{"$f":"SUM(H592:I592)","v":5}]
[null,null,null,null,null,null,"Totals",{"$f":"SUM(H591:H592)","v":3},{"$f":"SUM(I591:I592)","v":7},{"$f":"SUM(H593:I593)","v":10}]
[null,"4) From Pre-determined Probabilities"]
[null,"For a randomly selected Seattle visitor calculate the probability"]
[null,"that they visited the SN or PPM."]
[null,"P(SN)",null,0.5]
[null,"P(PPM)",null,0.7]
[null,"P(SS AND PPM)",null,0.4]
[null,"P(SN OR PPM)",null,null,{"$f":"D597+D598-D599","v":0.79999999999999993},{"$f":"_xlfn.IFNA(\" \"&D597&\"+\"&D598&\"-\"&D599,\"\")","v":" 0.5+0.7-0.4"}]
[null,"OR might be shown as: P(At least 1 site), or, P(1 or more sites)"]
[]
[]
[null,"Conditional Probability"]
[null,"The probability of an event given that another related event has already occurred."]
[null,"After the first event has occurred the sample space has changed (gotten smaller)."]
[null,"The two events that make up the Conditional Probability are considered dependent."]
[null,"Notation: P(A | B) = \"Probability of event A, given that event B has already occurred\".   \"|\" = \" given that\"."]
[null,"Examples:"]
[null,"1) This is not conditional probability:"]
[null,"What is probability of pulling one Queen card from a randomly shuffled deck of 52 cards?"]
[null,"There are 4 matching sample points: Q©, Q§, Qª, Q¨"]
[null,"When you calculated the probability, the full Sample Space is intact. Sample Space = 52 cards."]
[null,"P(Pull 1 Queen from deck of cards) = P(Q1) = 4/52"]
[]
[null,"2) This IS conditional probability:"]
[null,"Given that you pulled a Spade Queen card (Qª) as your first card, what is the probability that you can pull a Queen card in the second try?"]
[null,"There are 3 matching sample points: Q©, Q§, Q¨"]
[null,"When you calculated the probability, the Sample Space has changed. Sample Space = 51 cards."]
[null,"P(Pull second Queen given that you already pulled a Queen) = P(Q2 | Q1) = 3/51"]
[null,"The events \"Pulling a Second Queen\" and \"Pulling a First Queen\" are dependent events."]
[]
[null,"3) Calculate the probability that a randomly selected American uses Facebook given that they use YouTube."]
[null,"A random survey of American social media use was conducted and the results are presented in a cross tab report. From the report, calculate the probability that a randomly selected American uses Facebook given that they use YouTube. Said a different way: If a randomly selected American uses YouTube, what is probability that they also use Facebook? "]
[null,null,null,null,null,"Frequency","YouTube"]
[null,null,null,null,null,"Facebook","Not Use YT","Use YT","Total"]
[null,null,null,"Facebook = FB",null,"Not Use FB",16,46,62]
[null,null,null,"YouTube = YT",null,"Use FB",22,116,138]
[null,null,null,null,null,"Total",38,162,200]
[]
[null,"For this problem, the frequencies are given to you, but you can not use the full Sample Space of 200. Because the question askes you to isolate your calculation to just the sample space for YouTube, the Sample Space changes, the denominator that you use is the total number of people who use YouTube, 162."]
[]
[null,"P(Use YT) =",null,null,{"$f":"H629/I629","v":0.81},{"$f":"_xlfn.IFNA(\" \"&H629&\"/\"&$I$629,\"\")","v":" 162/200"},null,"Sample Space not change"]
[null,"P(Use FB AND Use YT) =",null,null,{"$f":"H628/I629","v":0.57999999999999996},{"$f":"_xlfn.IFNA(\" \"&H628&\"/\"&$I$629,\"\")","v":" 116/200"},null,"Sample Space not change"]
[null,"P(Use FB | Use YT) =",null,null,{"$f":"H628/H629","v":0.71604938271604934},{"$f":"_xlfn.IFNA(\" \"&H628&\"/\"&H629,\"\")","v":" 116/162"},null,"ç Sample Space DOES change"]
[null,"P(Use YT | Use FB) =",null,null,{"$f":"H628/I628","v":0.84057971014492749},{"$f":"_xlfn.IFNA(\" \"&H628&\"/\"&I628,\"\")","v":" 116/138"},null,"ç Sample Space DOES change"]
[]
[null,"Conditional Probability Rule:"]
[null,"P(A | B) = P(A AND B)/P(B) = \"Probability Event A occurs given that Event B has already occurred\"."]
[null,"P(B | A) = P(A AND B)/P(A) =  \"Probability Event B occurs given that Event A has already occurred\"."]
[null,"Textbook notation:"]
[null,"P(A | B) = P(A ∩ B)/P(B) = ",null,null,null,"Joint Probability Table",null,null,null,"AND %"]
[null,"P(B | A) = P(A ∩ B)/P(A) =",null,null,null,"Probability","YouTube"]
[null,null,null,null,null,"Facebook","Not Use YT","Use YT","Total"]
[null,"P(Use FB | Use YT) = ",null,{"$f":"H646/H647","v":0.71604938271604923},null,"Not Use FB",{"$f":"G627:I629/I629","v":0.08},0.23,0.31]
[null,null,null,{"$f":"_xlfn.IFNA(\" \"&H646&\"/\"&H647,\"\")","v":" 0.58/0.81"},null,"Use FB",0.11,0.57999999999999996,0.69]
[null,"P(Use YT | Use FB) =",null,{"$f":"H646/I646","v":0.84057971014492749},null,"Total",0.19,0.81,1]
[null,null,null,{"$f":"_xlfn.IFNA(\" \"&H646&\"/\"&I646,\"\")","v":" 0.58/0.69"}]
[null,null,null,null,null,null,null,null,null,"Marginal %"]
[]
[]
[null,"Joint Probability Tables"]
[null,"Joint Probability Tables are cross tabulated tables that that have row and column header conditions and show AND Logical Test Probabilities (Joint Probabilities) on this inside of the table, Single Condition Probabilities (Marginal Probabilities) in the row and column total sections."]
[]
[null,null,"Joint Probability Table",null,null,null,"AND % (Joint Probability)"]
[null,null,"Probability","YouTube"]
[null,null,"Facebook","Not Use YT","Use YT","Total"]
[null,null,"Not Use FB",{"$f":"G627:I629/I629","v":0.08},0.23,0.31]
[null,null,"Use FB",0.11,0.57999999999999996,0.69]
[null,null,"Total",0.19,0.81,1]
[]
[null,null,null,null,null,null,"Marginal % (Single Condition Prob.)"]
[null,"Examples:"]
[null,"1) Create Joint Probability from a proper data set"]
[]
[null,"When you have a proper data set with records of data, you can use the PivotTable feature to create a Cross Tabulated Frequency Distribution with the Show Values As % of Grand Total calculation."]
[]
[null,null,"Survey Data:",null,null,"Joint Probability created with PivotTable:"]
[]
[null,null,"Facebook","YouTube",null,"Joint Prob.","YT"]
[null,null,"Use FB","Use YT",null,"FB","Not Use YT","Use YT","Grand Total"]
[null,null,"Not Use FB","Use YT",null,"Not Use FB",0.08,0.23,0.31]
[null,null,"Not Use FB","Not Use YT",null,"Use FB",0.11,0.57999999999999996,0.69]
[null,null,"Use FB","Not Use YT",null,"Grand Total",0.19,0.81,1]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Use FB","Not Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Not Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[null,null,"Not Use FB","Use YT"]
[null,null,"Use FB","Use YT"]
[]
[null,"2) If you are given a cross tabulated report, the fastest way to create a Joint Probability Table is to use a Spilled Array Formula."]
[null,null,null,null,"Report given to you:","Frequency","YouTube"]
[null,null,null,null,null,"Facebook","Not Use YT","Use YT","Total"]
[null,null,null,"Facebook = FB",null,"Not Use FB",16,46,62]
[null,null,null,"YouTube = YT",null,"Use FB",22,116,138]
[null,null,null,null,null,"Total",38,162,200]
[null,"Steps to create Joint Probability Table:"]
[null,"1) Copy first report",null,null,null,"Frequency","YouTube"]
[null,"2) Delete numbers",null,null,null,"Facebook","Not Use YT","Use YT","Total"]
[null,"3) Create spilled array formula",null,null,null,"Not Use FB",{"$f":"G875:I877/I877","v":0.08},0.23,0.31]
[null,null,null,null,null,"Use FB",0.11,0.57999999999999996,0.69]
[null,null,null,null,null,"Total",0.19,0.81,1]
[]
[null,null,null,null,{"$f":"_xlfn.IFNA(\"Joint Probability Table Formula: \"&_xlfn.FORMULATEXT(G881),\"\")","v":"Joint Probability Table Formula: =G875:I877/I877"}]
[]
[]
[null,"Independent Events"]
[null,"Two events are independent if the probability of one event is not affected by the occurrence of the other."]
[]
[null,"Examples of Independent Events:"]
[null,"1) Rolling one die does not affect the roll of the next die."]
[]
[null,"2) Whether or not Alphabet stock (Google) goes up in a day does not affect whether or not Safeway stock goes up in that same day."]
[]
[null,"Rule of Independence"]
[null,"P(A | B) = P(A) , B has no affect on A."]
[null,"P(B | A) = P(B) , A has no affect on B."]
[null,"Otherwise the events are dependent."]
[null,"Examples of the Rule of Independent:"]
[]
[null,"1) P(Roll 6 on Second Roll of Die) = P(Roll 6 on Second Roll of Die | Rolled 6 on First Roll of Die) = 1/6"]
[]
[null,"2) The probability of making a sale for any one sales call is 0.15. Each sales call is an independent event.\nP(Sale on Call 2) = P(Sales on Call 2 | Sale on Call 1) = 0.15."]
[]
[null,"Multiplication Law of Probability (AND Logical Test / *)"]
[null,"Multiplication Law is used to calculate the probability of the intersection of events (probability of an AND Logical Test)."]
[null,"Multiplication rule for dependent events:",null,null,null,"Textbook notation:"]
[null,"P(A AND B) = P(B)*P(A | B)",null,null,null,"P(A ∩ B) = P(B)*P(A | B)"]
[null,"P(A AND B) = P(A)*P(B | A)",null,null,null,"P(A ∩ B) = P(A)*P(B | A)"]
[null,"Multiplication rule for independent events:"]
[null,"P(A AND B) = P(A)*P(B)",null,null,null,"P(A ∩ B) = P(A AND B) = P(A)*P(B)"]
[]
[null,"Example of Multiplying Dependent Events to calculate P(A AND B):"]
[]
[null,"1) Calculate the probability that you can pull two straight Queens from a deck of cards (without replacement)."]
[]
[null,null,"Population size (# cards in deck) = number_pop =",null,null,null,null,52]
[null,null,"Success in Population (# Queens) = population_s =",null,null,null,null,4]
[null,null,"Sample Size (cards pulled in successions) = number_sample =",null,null,null,null,2]
[null,null,"Success in Sample (# Queens) = sample_s =",null,null,null,null,2]
[]
[null,"P(Pull Two Straight Queens from Deck of Cards Without Replacement) ="]
[null,"P(Q2 AND Q1) = P(Q1)* P(Q2 | Q1) =",null,null,null,null,null,{"$f":"H919/H918*(H919-1)/(H918-1)","v":4.5248868778280547E-3},{"$f":"_xlfn.IFNA(H919&\"/\"&H918&\"*(\"&H919&\"-1)/(\"&H918&\"-1)\",\"\")","v":"4/52*(4-1)/(52-1)"}]
[null,null,null,null,null,null,null,{"$f":"_xlfn.HYPGEOM.DIST(H921,H920,H919,H918,0)","v":4.5248868778280521E-3}]
[null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(\" HYPGEOM.DIST(\"&H921&\",\"&H920&\",\"&H919&\",\"&H918&\",0)\",\"\")","v":" HYPGEOM.DIST(2,2,4,52,0)"}]
[]
[null,"Examples of Multiplying Independent Events to calculate P(A AND B):"]
[]
[null,"If the probability for a sale for any particular sales call is 0.15, and one sales call does not affect the next, then the probability of make a sale for the first call and a sale for the second call is:\nP(s)*P(s) = 0.15*0.15 = 0.0225"]
[]
[null,"Rule of Independence using Multiplication:"]
[null,"P(A AND B) = P(A)*P(B), where events A and B are independent. Otherwise the events are dependent."]
[null,"Example:"]
[null,"If P(G) = 0.65, P(S) = 0.35, P(G AND S) = 0.2275, are the events independent? Yes because 0.65*0.35 = 0.2275."]
[]
[null,"Mutually Exclusive vs. Independence"]
[null,"Don't confuse \"Mutually Exclusive\" (events have no sample points in common; if one event occurs, the other did not) and \"Independence\" (the two events exist, but are not related). Two non-zero probabilities cannot be both mutually exclusive and independent: Independence means two events exist, but are not related; whereas, Mutual Exclusivity means when one event occurs, the other cannot."]
[]
[]
[null,"Using the Multiplication Law of Probability"]
[null,"Multiplication rule for dependent events:"]
[null,"P(A AND B) = P(B)*P(A | B)"]
[null,"P(A AND B) = P(A)*P(B | A)"]
[null,"Multiplication rule for independent events:"]
[null,"P(A AND B) = P(A)*P(B)"]
[null,"4 examples of calculating the probability for an AND Logical Test:"]
[null,"1) Calculate the probability that both Alphabet stock and Safeway stock will go up next year."]
[null,"2) From a Cross Tabulated Report on American Social Media create a Probability Tree on worksheet."]
[null,"3) From a Cross Tabulated Report on American Social Media create a Probability Tree on paper."]
[null,"4) From a Cross Tabulated Report on Heart Attack & Smoking create a Probability Tree on paper."]
[]
[null,"1) The probability that Alphabet stock (Google) will go up next year is 0.65 and the probability that Safeway stock will go up next year is 0.35. What is probability that both will go up. Assume events are independent."]
[]
[null,null,null,"P(Alphabet stock will go up in 2023)",null,null,null,0.65]
[null,null,null,"P(Safeway will go up in 2023)",null,null,null,0.35]
[null,null,null,"P(Both will go up in 2023)",null,null,null,{"$f":"H956*H955","v":0.22749999999999998},{"$f":"\" \"&H955&\"*\"&H956","v":" 0.65*0.35"}]
[]
[null,"2) A random survey of American social media use was conducted. The random experiment will be to first ask: \"Do you use YouTube, Yes, or No?\". The second question will be to ask: \"Do you use Facebook, Yes, or No?\". From a Cross Tab Report shown below, create a Probability Tree that shows Root (Do you use YouTube?), Conditional (Do you use Facebook?) and Joint Probabilities (Do you use both?)."]
[]
[null,null,"Frequency","YouTube"]
[null,null,"Facebook","Not Use YT","Use YT","Total"]
[null,null,"Not Use FB",16,46,62]
[null,null,"Use FB",22,116,138,null,"Multiplication Law of Probability"]
[null,null,"Total",38,162,200,null,"ê","ê","ê"]
[]
[null,"Marginal Probabilities",null,null,"Conditional Probabilities",null,null,"Joint Probabilities (AND)"]
[]
[null,"Use YouTube?",null,null,"Use Facebook?",null,null,"Use Both"]
[]
[null,null,null,null,"Yes =",{"$f":"E964&\"/\"&E965","v":"116/162"},{"$f":"E964/E965","v":0.71604938271604934},{"$f":"$C$974&\"*\"&F971&\" = \"&CHAR(10)&E964&\"/\"&F965","v":"162/200*116/162 = \n116/200"},null,{"$f":"D974*G971","v":0.57999999999999996}]
[]
[]
[null,"Yes =",{"$f":"E965&\"/\"&F965","v":"162/200"},{"$f":"E965/F965","v":0.81}]
[]
[]
[null,null,null,null,"No =",{"$f":"E963&\"/\"&E965","v":"46/162"},{"$f":"E963/E965","v":0.2839506172839506},{"$f":"$C$974&\"*\"&F977&\" = \"&CHAR(10)&E963&\"/\"&F965","v":"162/200*46/162 = \n46/200"},null,{"$f":"D974*G977","v":0.23}]
[]
[]
[]
[null,null,null,null,"Yes =",{"$f":"D964&\"/\"&D965","v":"22/38"},{"$f":"D964/D965","v":0.57894736842105265},{"$f":"$C$984&\"*\"&F981&\" = \"&CHAR(10)&D964&\"/\"&F965","v":"38/200*22/38 = \n22/200"},null,{"$f":"D984*G981","v":0.11}]
[]
[]
[null,"No =",{"$f":"D965&\"/\"&F965","v":"38/200"},{"$f":"D965/F965","v":0.19}]
[]
[]
[null,null,null,null,"No =",{"$f":"D963&\"/\"&D965","v":"16/38"},{"$f":"D963/D965","v":0.42105263157894735},{"$f":"$C$984&\"*\"&F987&\" = \"&CHAR(10)&D963&\"/\"&F965","v":"38/200*16/38 = \n16/200"},null,{"$f":"D984*G987","v":0.08}]
[]
[]
[]
[null,"3) A random survey of American social media use was conducted. From a Cross Tab Report, create a Probability Tree that shows Root, Conditional and Joint Probabilities on paper:"]
[]
[null,null,"Frequency","YouTube"]
[null,null,"Facebook","Not Use YT","Use YT","Total"]
[null,null,"Not Use FB",16,46,62]
[null,null,"Use FB",22,116,138]
[null,null,"Total",38,162,200]
[]
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[null,"4) A random survey of Americans concerning heart attacks and smoking was conducted. From a Cross Tabulated Report on Heart Attack & Smoking create a Probability Tree on paper."]
[]
[null,null,"Frequency","Heart Attack"]
[null,null,"Smoke","Yes","No","Total"]
[null,null,"No",30,220,{"$f":"SUM(D1042:E1042)","v":250}]
[null,null,"Moderate",60,65,{"$f":"SUM(D1043:E1043)","v":125}]
[null,null,"Heavy",90,35,{"$f":"SUM(D1044:E1044)","v":125}]
[null,null,"Total",{"$f":"SUM(D1042:D1044)","v":180},{"$f":"SUM(E1042:E1044)","v":320},{"$f":"SUM(D1045:E1045)","v":500}]
[]
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[null,"Using Multiplication Law and Bayes' Theorem, Tabular Method can be used:"]
[]
[null,"Example 1:"]
[null,"You're about to take CPA exam, and you heard from last exam that the pass rate was 25%"]
[null,"P(Pass)",null,0.25]
[null,"P(Not Pass)",null,{"$f":"1-D1184","v":0.75},{"$f":"\" 1 - \"&D1184","v":" 1 - 0.25"}]
[null,"Your plan is to take a preparation course before taking the CPA exam, and therefore you would like to know the probability P(Pass | Took Prep Course)."]
[null,"Then you get new information from a survey that asked people who passed exam, whether or not they took a Preparation Course for the CPA exam:"]
[null,"P(Took Prep Course | Pass)",null,null,0.6]
[null,"P(Took Prep Course | Not Pass)",null,null,0.31]
[]
[null,"For this textbook, these probabilities are given",null,null,null,null,"Use Multiplication Rule to get AND"]
[null,"Prior (Marginal)",null,"Conditional",null,null,"Joint (AND)"]
[null,"P(Pass)",{"$f":"D1184","v":0.25},"P(Took Prep Course | Pass)",null,{"$f":"E1188","v":0.6},"P(Pass AND Took Prep Course)",null,{"$f":"C1193*F1193","v":0.15},{"$f":"\" \"&C1193&\"*\"&F1193","v":" 0.25*0.6"}]
[null,"P(Not Pass)",0.75,"P(Took Prep Course | Not Pass)",null,0.31,"P(Not Pass AND Took Prep Course)",null,{"$f":"C1194*F1194","v":0.23249999999999998},{"$f":"\" \"&C1194&\"*\"&F1194","v":" 0.75*0.31"}]
[null,"Total",1,null,null,null,null,"Total = Probability Took Prep Course =>",{"$f":"SUM(I1193:I1194)","v":0.38249999999999995}]
[]
[null,null,null,"Use \"Concept: compare parts to whole\", or Conditional Probability Rule."]
[null,null,null,null,null,null,"Posterior (Revised Probabilities)"]
[null,null,null,null,null,null,"P(Pass |\nTook Prep Course)",null,{"$f":"I1193/I1195","v":0.39215686274509809},{"$f":"\" \"&I1193&\"/\"&I1194","v":" 0.15/0.2325"}]
[null,null,null,null,null,null,"P(Pass |\nTook Prep Course)",null,{"$f":"D1184*E1188/SUMPRODUCT(D1184:D1185,E1188:E1189)","v":0.39215686274509809}]
[null,null,null,null,null,null,{"$f":"\" \"&D1184&\"*\"&E1188&\"/SUMPRODUCT(\"&_xlfn.ARRAYTOTEXT(D1184:D1185,1)&\",\"&_xlfn.ARRAYTOTEXT(E1188:E1189,1)&\")\"","v":" 0.25*0.6/SUMPRODUCT({0.25;0.75},{0.6;0.31})"}]
[]
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[null,"If we had full data set, then we can easily use the PivotTable tool to create a Joint Probability Table and then create the conditional probability needed for Bayes Theorem:"]
[]
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[null,"Example 2:"]
[]
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[null,"FILTER Function"]
[null,"The FILTER array function allows you to filter a set of values to show only that values that meet a logical test. The array argument contains the values that you want to filter. The include argument requires an array of TRUE and FALSE values (same dimension as array argument values) to indicate which values to keep (TRUE) and with ones to filter out (FALSE).\n\nFor an OR Logical Test, use addition,  + operation, like: =FILTER(H54:I63,(H54:H63=G87)+(I54:I63=G88))\n\nFor an AND Logical Test, use multiplication, * operator, like: =FILTER(H54:I63,(H54:H63=G87)*(I54:I63=G88))"]
[null,"COUNTIFS function"]
[null,"The COUNTIFS function makes a conditional count calculation based on one or more logical tests. The criteria_range argument contains the full range with all the conditional items. The criteria argument contains the conditions for counting items from the criteria_range1 argument.\n\nIf you use a single condition like with: =COUNTIFS(H3:H12,G16), you are performing a Single Condition Logical Test.\n\nIf you use two or more conditions like with: =COUNTIFS(M31:M40,G47,N31:N40,G48), you are performing an AND Logical Test.\n\nIf you need to use a comparative operator with the condition, you must join the comparative operator to the cell with the condition, like: \"<>\"&G21. Example for this formula counts items that are not whatever the value in cell G21 is.\n\nYou can have up to 127 pairs of criteria_rangeN criteriaN arguments that will run an AND Logical Test to make the conditional count calculation."]
[null,"Comparative Operator Note:"]
[null,"* When using comparative operators in functions like COUNTIFS, SUMIFS, AVERAGEIFS, MINIFS and MAXIFS, you must join the comparative operator to the cell with the condition, like: \">\"&J28.\n* But when you use a comparative operator in a formula that makes a direct logical test formula calculation, you do not use quotes or an ampersand (join operator), like: H54:H63=G87."]

{"sheet":"Restaurant","index":9,"n_rows":112,"n_cols":11,"rows_kept":112,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Isaac's Italian Restaurant has 4 banquet rooms that are used on weekends"]
[null,"Data collected: Number of rooms used in a day over the past year."]
[null,"Chapter 5: Empirical Discrete Distibution"]
[]
[null,null,"X = Random Discrete Variable = Number of Rooms Used for the Day"]
[]
[null,"Date","# Rooms Used in Day","Day",null,null,null,null,"# Rooms Used in Day","Frequency","% Frequency"]
[null,"2020-01-04",1,{"$f":"TEXT(B9,\"ddd\")","v":"Sat"},null,null,null,null,0,2,1.9230769230769232E-2]
[null,"2020-01-05",2,{"$f":"TEXT(B10,\"ddd\")","v":"Sun"},null,null,null,null,1,21,0.20192307692307693]
[null,{"$f":"B9+7","v":"2020-01-11"},4,"Sat",null,null,null,null,2,45,0.43269230769230771]
[null,{"$f":"B10+7","v":"2020-01-12"},3,"Sun",null,null,null,null,3,28,0.26923076923076922]
[null,"2020-01-18",3,"Sat",null,null,null,null,4,8,7.6923076923076927E-2]
[null,"2020-01-19",2,"Sun",null,null,null,null,"Grand Total",104,1]
[null,"2020-01-25",2,"Sat"]
[null,"2020-01-26",2,"Sun"]
[null,"2020-02-01",4,"Sat"]
[null,"2020-02-02",1,"Sun"]
[null,"2020-02-08",2,"Sat"]
[null,"2020-02-09",2,"Sun"]
[null,"2020-02-15",2,"Sat"]
[null,"2020-02-16",1,"Sun"]
[null,"2020-02-22",1,"Sat"]
[null,"2020-02-23",2,"Sun"]
[null,"2020-02-29",2,"Sat"]
[null,"2020-03-01",2,"Sun"]
[null,"2020-03-07",4,"Sat"]
[null,"2020-03-08",2,"Sun"]
[null,"2020-03-14",3,"Sat"]
[null,"2020-03-15",2,"Sun"]
[null,"2020-03-21",3,"Sat"]
[null,"2020-03-22",3,"Sun"]
[null,"2020-03-28",2,"Sat"]
[null,"2020-03-29",2,"Sun"]
[null,"2020-04-04",2,"Sat"]
[null,"2020-04-05",2,"Sun"]
[null,"2020-04-11",3,"Sat"]
[null,"2020-04-12",3,"Sun"]
[null,"2020-04-18",1,"Sat"]
[null,"2020-04-19",1,"Sun"]
[null,"2020-04-25",3,"Sat"]
[null,"2020-04-26",3,"Sun"]
[null,"2020-05-02",1,"Sat"]
[null,"2020-05-03",3,"Sun"]
[null,"2020-05-09",2,"Sat"]
[null,"2020-05-10",3,"Sun"]
[null,"2020-05-16",1,"Sat"]
[null,"2020-05-17",1,"Sun"]
[null,"2020-05-23",2,"Sat"]
[null,"2020-05-24",1,"Sun"]
[null,"2020-05-30",1,"Sat"]
[null,"2020-05-31",4,"Sun"]
[null,"2020-06-06",3,"Sat"]
[null,"2020-06-07",1,"Sun"]
[null,"2020-06-13",3,"Sat"]
[null,"2020-06-14",2,"Sun"]
[null,"2020-06-20",2,"Sat"]
[null,"2020-06-21",2,"Sun"]
[null,"2020-06-27",2,"Sat"]
[null,"2020-06-28",3,"Sun"]
[null,"2020-07-04",3,"Sat"]
[null,"2020-07-05",2,"Sun"]
[null,"2020-07-11",2,"Sat"]
[null,"2020-07-12",2,"Sun"]
[null,"2020-07-18",1,"Sat"]
[null,"2020-07-19",2,"Sun"]
[null,"2020-07-25",2,"Sat"]
[null,"2020-07-26",3,"Sun"]
[null,"2020-08-01",0,"Sat"]
[null,"2020-08-02",3,"Sun"]
[null,"2020-08-08",4,"Sat"]
[null,"2020-08-09",3,"Sun"]
[null,"2020-08-15",1,"Sat"]
[null,"2020-08-16",2,{"$f":"TEXT(B74,\"ddd\")","v":"Sun"}]
[null,"2020-08-22",2,"Sat"]
[null,{"$f":"B74+7","v":"2020-08-23"},1,"Sun"]
[null,"2020-08-29",2,"Sat"]
[null,"2020-08-30",3,"Sun"]
[null,"2020-09-05",2,"Sat"]
[null,"2020-09-06",2,"Sun"]
[null,"2020-09-12",3,"Sat"]
[null,"2020-09-13",3,"Sun"]
[null,"2020-09-19",1,"Sat"]
[null,"2020-09-20",1,"Sun"]
[null,"2020-09-26",2,"Sat"]
[null,"2020-09-27",1,"Sun"]
[null,"2020-10-03",3,"Sat"]
[null,"2020-10-04",3,"Sun"]
[null,"2020-10-10",2,"Sat"]
[null,"2020-10-11",2,"Sun"]
[null,"2020-10-17",2,"Sat"]
[null,"2020-10-18",2,"Sun"]
[null,"2020-10-24",1,"Sat"]
[null,"2020-10-25",2,"Sun"]
[null,"2020-10-31",4,"Sat"]
[null,"2020-11-01",0,"Sun"]
[null,"2020-11-07",4,"Sat"]
[null,"2020-11-08",2,"Sun"]
[null,"2020-11-14",1,"Sat"]
[null,"2020-11-15",3,"Sun"]
[null,"2020-11-21",4,"Sat"]
[null,"2020-11-22",3,"Sun"]
[null,"2020-11-28",3,"Sat"]
[null,"2020-11-29",2,"Sun"]
[null,"2020-12-05",1,"Sat"]
[null,"2020-12-06",3,"Sun"]
[null,"2020-12-12",2,"Sat"]
[null,"2020-12-13",2,"Sun"]
[null,"2020-12-19",2,"Sat"]
[null,"2020-12-20",3,"Sun"]
[null,"2020-12-26",2,"Sat"]
[null,"2020-12-27",2,"Sun"]

{"sheet":"Dice","index":10,"n_rows":18,"n_cols":3,"rows_kept":18,"cut":false,"hidden":false,"merged":[]}
[]
[]
[]
[null,"Use Table Format to visualize Sample Space and show all experimental outcomes (sample points):"]
[]
[null,"Example of table to visualize all sample points for a two-step random experiment of throwing two die:"]
[]
[null,null,"Die1/Die2"]
[]
[]
[]
[]
[]
[]
[]
[null,null,{"$f":"_xlfn.IFNA(\"Die 1 formula: \"&_xlfn.FORMULATEXT(C9),\"\")","v":""}]
[null,null,{"$f":"_xlfn.IFNA(\"Die 2 formula: \"&_xlfn.FORMULATEXT(D8),\"\")","v":""}]
[null,null,{"$f":"_xlfn.IFNA(\"Inside formula: \"&_xlfn.FORMULATEXT(D9),\"\")","v":""}]

{"sheet":"Dice (an)","index":11,"n_rows":21,"n_cols":19,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
[]
[]
[]
[null,"Use Table Format to visualize Sample Space and show all experimental outcomes (sample points):"]
[]
[null,"Example of table to visualize all sample points for a two-step random experiment of throwing two die:"]
[]
[null,null,"Die1/Die2",{"$f":"_xlfn.SEQUENCE(,6)","v":1},2,3,4,5,6]
[null,null,{"$f":"_xlfn.SEQUENCE(6)","v":1},{"$f":"\"(\"&_xlfn.ANCHORARRAY(C9)&\", \"&_xlfn.ANCHORARRAY(D8)&\") = \"&_xlfn.ANCHORARRAY(C9)+_xlfn.ANCHORARRAY(D8)","v":"(1, 1) = 2"},"(1, 2) = 3","(1, 3) = 4","(1, 4) = 5","(1, 5) = 6","(1, 6) = 7",null,null,null,null,"From comments at YouTube from ExcelLambda (just for fun):"]
[null,null,2,"(2, 1) = 3","(2, 2) = 4","(2, 3) = 5","(2, 4) = 6","(2, 5) = 7","(2, 6) = 8",null,null,null,null,{"$f":"_xlfn.MAKEARRAY(6,6,_xlfn.LAMBDA(_xlpm.r,_xlpm.c,\"(\"&_xlpm.r&\", \"&_xlpm.c&\") = \"&_xlpm.r+_xlpm.c))","v":"(1, 1) = 2"},"(1, 2) = 3","(1, 3) = 4","(1, 4) = 5","(1, 5) = 6","(1, 6) = 7"]
[null,null,3,"(3, 1) = 4","(3, 2) = 5","(3, 3) = 6","(3, 4) = 7","(3, 5) = 8","(3, 6) = 9",null,null,null,null,"(2, 1) = 3","(2, 2) = 4","(2, 3) = 5","(2, 4) = 6","(2, 5) = 7","(2, 6) = 8"]
[null,null,4,"(4, 1) = 5","(4, 2) = 6","(4, 3) = 7","(4, 4) = 8","(4, 5) = 9","(4, 6) = 10",null,null,null,null,"(3, 1) = 4","(3, 2) = 5","(3, 3) = 6","(3, 4) = 7","(3, 5) = 8","(3, 6) = 9"]
[null,null,5,"(5, 1) = 6","(5, 2) = 7","(5, 3) = 8","(5, 4) = 9","(5, 5) = 10","(5, 6) = 11",null,null,null,null,"(4, 1) = 5","(4, 2) = 6","(4, 3) = 7","(4, 4) = 8","(4, 5) = 9","(4, 6) = 10"]
[null,null,6,"(6, 1) = 7","(6, 2) = 8","(6, 3) = 9","(6, 4) = 10","(6, 5) = 11","(6, 6) = 12",null,null,null,null,"(5, 1) = 6","(5, 2) = 7","(5, 3) = 8","(5, 4) = 9","(5, 5) = 10","(5, 6) = 11"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"(6, 1) = 7","(6, 2) = 8","(6, 3) = 9","(6, 4) = 10","(6, 5) = 11","(6, 6) = 12"]
[null,null,{"$f":"_xlfn.IFNA(\"Die 1 formula: \"&_xlfn.FORMULATEXT(C9),\"\")","v":"Die 1 formula: =SEQUENCE(6)"}]
[null,null,{"$f":"_xlfn.IFNA(\"Die 2 formula: \"&_xlfn.FORMULATEXT(D8),\"\")","v":"Die 2 formula: =SEQUENCE(,6)"}]
[null,null,{"$f":"_xlfn.IFNA(\"Inside formula: \"&_xlfn.FORMULATEXT(D9),\"\")","v":"Inside formula: =\"(\"&C9#&\", \"&D8#&\") = \"&C9#+D8#"}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"From comments at YouTube from DRSteele (just for fun):"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.UNICHAR(RANDBETWEEN(0,5)+9856)","v":"⚄"},"Hit F9 key to roll dice"]

{"sheet":"Counting","index":12,"n_rows":193,"n_cols":21,"rows_kept":193,"cut":false,"hidden":false,"merged":[[56,1,56,9],[59,1,59,9],[68,1,68,9],[69,1,69,9],[71,1,71,9],[54,1,54,9],[10,1,10,9],[18,1,18,9],[27,1,27,9],[34,4,39,5],[44,1,44,9]]}
[]
[null,"Counting Rule for Multi-Step Random Experiment"]
[null,"Total number of experimental outcomes (sample points) = size of sample space = n1 * n2 * … nk"]
[null,"k = Number of steps or trials in the random experiment"]
[null,"n1 = number of possible outcomes in step 1"]
[null,"n2 = number of possible outcomes in step 2"]
[null,"nk = number of possible outcomes in last step"]
[null,"Examples:"]
[null,"1) Roll two die. k = 2, n1 = 6, n2 = 6. Total experiments outcomes = 6*6 = 36"]
[]
[null,"2) Determine lock code with 3 spots and 10 digits. What are the number of total experimental outcomes (total possible lock codes)?"]
[]
[null,"Number slots for lock code:",null,null,"k",3]
[null,{"$f":"\"Digits: \"&_xlfn.TEXTJOIN(\", \",,_xlfn.SEQUENCE(,10))","v":"Digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10"},null,null,"n1",10]
[null,{"$f":"\"Digits: \"&_xlfn.TEXTJOIN(\", \",,_xlfn.SEQUENCE(,10))","v":"Digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10"},null,null,"n2",10]
[null,{"$f":"\"Digits: \"&_xlfn.TEXTJOIN(\", \",,_xlfn.SEQUENCE(,10))","v":"Digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10"},null,null,"n3",10]
[null,null,"Total lock possibilities:",null,null,null,{"$f":"_xlfn.IFNA(\" \"&F14&\"*\"&F15&\"*\"&F16&\" or \"&F14&\"^\"&F13,\"\")","v":" 10*10*10 or 10^3"}]
[]
[null,"3) Deli offers 2 rolls, 4 meats and 3 cheeses. k = 3, n1 = 2, n2 = 4, n3 = 3. What are the number of total experimental outcomes (total number of different sandwiches) if you get one of each?"]
[]
[null,"# steps in building sandwich:",null,null,"k",3]
[null,"Number rolls",null,null,"n1",2]
[null,"Number meats",null,null,"n2",4]
[null,null,null,null,"n3",3]
[null,null,"Total lock possibilities:",null,null,null,{"$f":"_xlfn.IFNA(\" \"&F22&\"*\"&F23&\"*\"&F24,\"\")","v":" 2*4*3"}]
[]
[]
[null,"Sometimes we have to decide on sample space with combinations or permutations, where you select n objects from a set of N objects."]
[]
[null,"Example of the difference between a Combination and a Permutation:"]
[null,"If we select the letters A, B, C, one after the other and you cannot repeat (example: A, A, A not allowed)"]
[]
[null,null,"Permutations",null,"Combinations"]
[null,null,"Order Matters",null,"Order Does Not Matter",null,"* You can pick the letters in any"]
[null,null,"A, B, C",null,"A, B, C",null,"order, but just one time."]
[null,null,"A, C, B"]
[null,null,"B, A, C"]
[null,null,"B, C, A"]
[null,null,"C, A, B"]
[null,null,"C, B, C"]
[null,"Total",{"$f":"COUNTA(C35:C40)","v":6},null,{"$f":"COUNTA(E35:E40)","v":1}]
[]
[]
[null,"Counting Rule for Combinations, Order Does Not Matter"]
[null,"When experiment involves selecting n objects from a set of N objects, and the order of the items is not considered, like: (2,1) is the same as (1,2), then:\nTotal number of experimental outcomes (sample points) = size of sample space ="]
[]
[]
[]
[null,"N = count of all objects (population)",null,null,null,null,7,"Population Size"]
[null,"n = count of  objects selected (sample size)",null,null,null,null,3,"Sample Size"]
[null,"In Excel use function: COMBIN(N,n)",null,null,null,null,null,"Total combinations"]
[null,null,null,null,null,null,{"$f":"_xlfn.IFNA(\"=COMBIN(\"&G49&\",\"&G50&\")\",\"\")","v":"=COMBIN(7,3)"}]
[null,"Note: Factorial (from your algebra class) is represented by ! Example: 5! = 5*4*3*2*1 = 120, and: 0! = 1."]
[null,"Examples:"]
[null,"1) Find all possible combinations of sample size 3 from a set of 7 numbers = 7!/(3!*(7-3)!) = (7*6*5*4*3*2*1)/(3*2*1*(4*3*2*1)) = (7*6*5)/(3*2*1*) = 7*5 = 35"]
[]
[null,"2) Find all combinations a for a basketball team that has 13 players and 5 can play in a game, assuming a player can play any position = 13!/(5!*(13-5) = (13*12*11*10*9)/(5*4*3*2*1) =\n(13*3*11*2*3)/2 = 1287"]
[]
[null,"Counting Rule for Permutations, Order Matters"]
[null,"When experiment involves selecting n objects from a set of N objects, and the order of the items is considered, like: (2,1) is different than (1,2), then:\nTotal number of experimental outcomes (sample points) = size of sample space = "]
[]
[]
[]
[null,"N = count of all objects (population)",null,null,null,null,5,"Population Size"]
[null,"n = count of  objects selected (sample size)",null,null,null,null,5,"Sample Size"]
[null,"In Excel use function: PERMUT(N,n)",null,null,null,null,null,"Total permutations"]
[null,null,null,null,null,null,{"$f":"_xlfn.IFNA(\"=PERMUT(\"&G64&\",\"&G65&\")\",\"\")","v":"=PERMUT(5,5)"}]
[null,"Examples:"]
[null,"1) Find total possible arrangements for 5 employees in 5 different offices = 5!/(5-5)! = (5*4*3*2*1)/0! = 120/1 = 120"]
[null,"2) Find total possible arrangements for 5 employees in 3 different offices = 5!/(5-3)! = (5*4*3*2*1)/2! = 120/2 = 60"]
[null,null,null,null,null,null,null,null,null,null,null,"Five Employees:",null,"Names:",null,"Permutations for 5 Offices:",null,null,null,"All Unique?",{"$f":"ROWS(_xlfn.UNIQUE(P74:T193))","v":120}]
[null,{"$f":"M73&\"   \"&M74","v":"   "},null,null,null,null,null,null,null,null,null,null,null,"June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone",null,"Office 1","Office 2","Office 3","Office 4","Office 5"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi",null,"June","Tyrone","Gigi","Dino","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino",null,"June","Tyrone","Gigi","Sioux","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux",null,"June","Tyrone","Dino","Gigi","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Tyrone","Dino","Sioux","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Tyrone","Sioux","Gigi","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Tyrone","Sioux","Dino","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Gigi","Tyrone","Dino","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Gigi","Tyrone","Sioux","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Gigi","Dino","Tyrone","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Gigi","Dino","Sioux","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Gigi","Sioux","Tyrone","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Gigi","Sioux","Dino","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Dino","Tyrone","Gigi","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Dino","Tyrone","Sioux","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Dino","Gigi","Tyrone","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Dino","Gigi","Sioux","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Dino","Sioux","Tyrone","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Dino","Sioux","Gigi","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Sioux","Tyrone","Gigi","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Sioux","Tyrone","Dino","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Sioux","Gigi","Tyrone","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Sioux","Gigi","Dino","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Sioux","Dino","Tyrone","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"June","Sioux","Dino","Gigi","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","June","Gigi","Dino","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","June","Gigi","Sioux","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","June","Dino","Gigi","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","June","Dino","Sioux","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","June","Sioux","Gigi","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","June","Sioux","Dino","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Gigi","June","Dino","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Gigi","June","Sioux","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Gigi","Dino","June","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Gigi","Dino","Sioux","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Gigi","Sioux","June","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Gigi","Sioux","Dino","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Dino","June","Gigi","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Dino","June","Sioux","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Dino","Gigi","June","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Dino","Gigi","Sioux","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Dino","Sioux","June","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Dino","Sioux","Gigi","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Sioux","June","Gigi","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Sioux","June","Dino","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Sioux","Gigi","June","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Sioux","Gigi","Dino","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Sioux","Dino","June","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tyrone","Sioux","Dino","Gigi","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","June","Tyrone","Dino","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","June","Tyrone","Sioux","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","June","Dino","Tyrone","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","June","Dino","Sioux","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","June","Sioux","Tyrone","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","June","Sioux","Dino","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Tyrone","June","Dino","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Tyrone","June","Sioux","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Tyrone","Dino","June","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Tyrone","Dino","Sioux","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Tyrone","Sioux","June","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Tyrone","Sioux","Dino","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Dino","June","Tyrone","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Dino","June","Sioux","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Dino","Tyrone","June","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Dino","Tyrone","Sioux","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Dino","Sioux","June","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Dino","Sioux","Tyrone","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Sioux","June","Tyrone","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Sioux","June","Dino","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Sioux","Tyrone","June","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Sioux","Tyrone","Dino","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Sioux","Dino","June","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Gigi","Sioux","Dino","Tyrone","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","June","Tyrone","Gigi","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","June","Tyrone","Sioux","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","June","Gigi","Tyrone","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","June","Gigi","Sioux","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","June","Sioux","Tyrone","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","June","Sioux","Gigi","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Tyrone","June","Gigi","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Tyrone","June","Sioux","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Tyrone","Gigi","June","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Tyrone","Gigi","Sioux","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Tyrone","Sioux","June","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Tyrone","Sioux","Gigi","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Gigi","June","Tyrone","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Gigi","June","Sioux","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Gigi","Tyrone","June","Sioux"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Gigi","Tyrone","Sioux","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Gigi","Sioux","June","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Gigi","Sioux","Tyrone","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Sioux","June","Tyrone","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Sioux","June","Gigi","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Sioux","Tyrone","June","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Sioux","Tyrone","Gigi","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Sioux","Gigi","June","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Dino","Sioux","Gigi","Tyrone","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","June","Tyrone","Gigi","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","June","Tyrone","Dino","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","June","Gigi","Tyrone","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","June","Gigi","Dino","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","June","Dino","Tyrone","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","June","Dino","Gigi","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Tyrone","June","Gigi","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Tyrone","June","Dino","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Tyrone","Gigi","June","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Tyrone","Gigi","Dino","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Tyrone","Dino","June","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Tyrone","Dino","Gigi","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Gigi","June","Tyrone","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Gigi","June","Dino","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Gigi","Tyrone","June","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Gigi","Tyrone","Dino","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Gigi","Dino","June","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Gigi","Dino","Tyrone","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Dino","June","Tyrone","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Dino","June","Gigi","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Dino","Tyrone","June","Gigi"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Dino","Tyrone","Gigi","June"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Dino","Gigi","June","Tyrone"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Dino","Gigi","Tyrone","June"]

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[]
[null,"Counting Rule for Multi-Step Random Experiment"]
[null,"Total number of experimental outcomes (sample points) = size of sample space = n1 * n2 * … nk"]
[null,"k = Number of steps or trials in the random experiment"]
[null,"n1 = number of possible outcomes in step 1"]
[null,"n2 = number of possible outcomes in step 2"]
[null,"nk = number of possible outcomes in last step"]
[null,"Examples:"]
[null,"1) Roll two die. k = 2, n1 = 6, n2 = 6. Total experiments outcomes = 6*6 = 36"]
[]
[null,"2) Determine lock code with 3 spots and 10 digits. What are the number of total experimental outcomes (total possible lock codes)?"]
[]
[null,"Number slots for lock code:",null,null,"k",3]
[null,{"$f":"\"Digits: \"&_xlfn.TEXTJOIN(\", \",,_xlfn.SEQUENCE(,10))","v":"Digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10"},null,null,"n1",10]
[null,{"$f":"\"Digits: \"&_xlfn.TEXTJOIN(\", \",,_xlfn.SEQUENCE(,10))","v":"Digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10"},null,null,"n2",10]
[null,{"$f":"\"Digits: \"&_xlfn.TEXTJOIN(\", \",,_xlfn.SEQUENCE(,10))","v":"Digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10"},null,null,"n3",10]
[null,null,"Total lock possibilities:",null,null,{"$f":"F14^F13","v":1000},{"$f":"_xlfn.IFNA(\" \"&F14&\"*\"&F15&\"*\"&F16&\" or \"&F14&\"^\"&F13,\"\")","v":" 10*10*10 or 10^3"}]
[]
[null,"3) Deli offers 2 rolls, 4 meats and 3 cheeses. k = 3, n1 = 2, n2 = 4, n3 = 3. What are the number of total experimental outcomes (total number of different sandwiches) if you get one of each?"]
[]
[null,"# steps in building sandwich:",null,null,"k",3]
[null,"Number rolls",null,null,"n1",2]
[null,"Number meats",null,null,"n2",4]
[null,null,null,null,"n3",3]
[null,null,"Total lock possibilities:",null,null,{"$f":"F22*F23*F24","v":24},{"$f":"_xlfn.IFNA(\" \"&F22&\"*\"&F23&\"*\"&F24,\"\")","v":" 2*4*3"}]
[]
[]
[null,"Sometimes we have to decide on sample space with combinations or permutations, where you select n objects from a set of N objects."]
[]
[null,"Example of the difference between a Combination and a Permutation:"]
[null,"If we select the letters A, B, C, one after the other and you cannot repeat (example: A, A, A not allowed)"]
[]
[null,null,"Permutations",null,"Combinations"]
[null,null,"Order Matters",null,"Order Does Not Matter",null,"* You can pick the letters in any"]
[null,null,"A, B, C",null,"A, B, C",null,"order, but just one time."]
[null,null,"A, C, B"]
[null,null,"B, A, C"]
[null,null,"B, C, A"]
[null,null,"C, A, B"]
[null,null,"C, B, C"]
[null,"Total",{"$f":"COUNTA(C35:C40)","v":6},null,{"$f":"COUNTA(E35:E40)","v":1}]
[]
[]
[null,"Counting Rule for Combinations, Order Does Not Matter"]
[null,"When experiment involves selecting n objects from a set of N objects, and the order of the items is not considered, like: (2,1) is the same as (1,2), then:\nTotal number of experimental outcomes (sample points) = size of sample space ="]
[]
[]
[]
[null,"N = count of all objects (population)",null,null,null,null,7,"Population Size"]
[null,"n = count of  objects selected (sample size)",null,null,null,null,3,"Sample Size"]
[null,"In Excel use function: COMBIN(N,n)",null,null,null,null,{"$f":"COMBIN(G49,G50)","v":35},"Total combinations"]
[null,null,null,null,null,null,{"$f":"_xlfn.IFNA(\"=COMBIN(\"&G49&\",\"&G50&\")\",\"\")","v":"=COMBIN(7,3)"}]
[null,"Note: Factorial (from your algebra class) is represented by ! Example: 5! = 5*4*3*2*1 = 120, and: 0! = 1."]
[null,"Examples:"]
[null,"1) Find all possible combinations of sample size 3 from a set of 7 numbers = 7!/(3!*(7-3)!) = (7*6*5*4*3*2*1)/(3*2*1*(4*3*2*1)) = (7*6*5)/(3*2*1*) = 7*5 = 35"]
[]
[null,"2) Find all combinations a for a basketball team that has 13 players and 5 can play in a game, assuming a player can play any position = 13!/(5!*(13-5) = (13*12*11*10*9)/(5*4*3*2*1) =\n(13*3*11*2*3)/2 = 1287"]
[]
[null,"Counting Rule for Permutations, Order Matters"]
[null,"When experiment involves selecting n objects from a set of N objects, and the order of the items is considered, like: (2,1) is different than (1,2), then:\nTotal number of experimental outcomes (sample points) = size of sample space = "]
[]
[]
[]
[null,"N = count of all objects (population)",null,null,null,null,5,"Population Size"]
[null,"n = count of  objects selected (sample size)",null,null,null,null,5,"Sample Size"]
[null,"In Excel use function: PERMUT(N,n)",null,null,null,null,{"$f":"PERMUT(G64,G65)","v":120},"Total permutations"]
[null,null,null,null,null,null,{"$f":"_xlfn.IFNA(\"=PERMUT(\"&G64&\",\"&G65&\")\",\"\")","v":"=PERMUT(5,5)"}]
[null,"Examples:"]
[null,"1) Find total possible arrangements for 5 employees in 5 different offices = 5!/(5-5)! = (5*4*3*2*1)/0! = 120/1 = 120"]
[null,"2) Find total possible arrangements for 5 employees in 3 different offices = 5!/(5-3)! = (5*4*3*2*1)/2! = 120/2 = 60"]
[null,null,null,null,null,null,null,null,null,null,null,"Five Employees:",null,"Names:",null,"Permutations for 5 Offices:",null,null,null,null,"All Unique?",{"$f":"ROWS(_xlfn.UNIQUE(P74:T193))","v":120}]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Tyrone","Gigi","June","Dino"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Tyrone","Gigi","Dino","June"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sioux","Gigi","Tyrone","June","Dino"]
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{"sheet":"Combin","index":14,"n_rows":42,"n_cols":11,"rows_kept":42,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Population",{"$f":"ROWS(B8:C14)","v":7},null,"Used in Chapter 7 (Central Limit Theorem)"]
[null,"Sample size",3]
[null,"Combinations",{"$f":"COMBIN(C2,C3)","v":35},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(C4),COLUMN(C4),4)&\": \"&_xlfn.FORMULATEXT(C4),\"\")","v":"C4: =COMBIN(C2,C3)"}]
[]
[]
[null,"Sales Rep","Sales",null,"Sales Rep 1","Sales Rep 2","Sales Rep 3","Sales 1","Sales 2","Sales 3","Xbar"]
[null,"Jo",185,null,"Jo","Sioux","Chin",{"$f":"_xlfn.XLOOKUP(E8:G42,B8:B14,C8:C14)","v":185},250,210,{"$f":"AVERAGE(H8:J8)","v":215}]
[null,"Sioux",250,null,"Jo","Sioux","Sheliadawn",185,250,310,{"$f":"AVERAGE(H9:J9)","v":248.33333333333334}]
[null,"Chin",210,null,"Jo","Sioux","Gigi",185,250,298,244.33333333333334]
[null,"Sheliadawn",310,null,"Jo","Sioux","Tyrone",185,250,402,279]
[null,"Gigi",298,null,"Jo","Sioux","Kip",185,250,370,268.33333333333331]
[null,"Tyrone",402,null,"Jo","Chin","Sheliadawn",185,210,310,235]
[null,"Kip",370,null,"Jo","Chin","Gigi",185,210,298,231]
[null,null,null,null,"Jo","Chin","Tyrone",185,210,402,265.66666666666669]
[null,null,null,null,"Jo","Chin","Kip",185,210,370,255]
[null,null,null,null,"Jo","Sheliadawn","Gigi",185,310,298,264.33333333333331]
[null,null,null,null,"Jo","Sheliadawn","Tyrone",185,310,402,299]
[null,null,null,null,"Jo","Sheliadawn","Kip",185,310,370,288.33333333333331]
[null,null,null,null,"Jo","Gigi","Tyrone",185,298,402,295]
[null,null,null,null,"Jo","Gigi","Kip",185,298,370,284.33333333333331]
[null,null,null,null,"Jo","Tyrone","Kip",185,402,370,319]
[null,null,null,null,"Sioux","Chin","Sheliadawn",250,210,310,256.66666666666669]
[null,null,null,null,"Sioux","Chin","Gigi",250,210,298,252.66666666666666]
[null,null,null,null,"Sioux","Chin","Tyrone",250,210,402,287.33333333333331]
[null,null,null,null,"Sioux","Chin","Kip",250,210,370,276.66666666666669]
[null,null,null,null,"Sioux","Sheliadawn","Gigi",250,310,298,286]
[null,null,null,null,"Sioux","Sheliadawn","Tyrone",250,310,402,320.66666666666669]
[null,null,null,null,"Sioux","Sheliadawn","Kip",250,310,370,310]
[null,null,null,null,"Sioux","Gigi","Tyrone",250,298,402,316.66666666666669]
[null,null,null,null,"Sioux","Gigi","Kip",250,298,370,306]
[null,null,null,null,"Sioux","Tyrone","Kip",250,402,370,340.66666666666669]
[null,null,null,null,"Chin","Sheliadawn","Gigi",210,310,298,272.66666666666669]
[null,null,null,null,"Chin","Sheliadawn","Tyrone",210,310,402,307.33333333333331]
[null,null,null,null,"Chin","Sheliadawn","Kip",210,310,370,296.66666666666669]
[null,null,null,null,"Chin","Gigi","Tyrone",210,298,402,303.33333333333331]
[null,null,null,null,"Chin","Gigi","Kip",210,298,370,292.66666666666669]
[null,null,null,null,"Chin","Tyrone","Kip",210,402,370,327.33333333333331]
[null,null,null,null,"Sheliadawn","Gigi","Tyrone",310,298,402,336.66666666666669]
[null,null,null,null,"Sheliadawn","Gigi","Kip",310,298,370,326]
[null,null,null,null,"Sheliadawn","Tyrone","Kip",310,402,370,360.66666666666669]
[null,null,null,null,"Gigi","Tyrone","Kip",298,402,370,356.66666666666669]

{"sheet":"Retrofit","index":15,"n_rows":27,"n_cols":8,"rows_kept":27,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Sound Home Earthquake Retrofitting",null,null,null,null,null,"Sample Points and Relative Frequency"]
[null,"Two steps for basic retrofit projects: Design and then Construction."]
[null,"Goal: The company needs to estimate the probability that it will take 1 month or less to complete a project."]
[null,"Past company records show these possibilities:"]
[null,"Step 1: Design. Usually it takes 1 or 2 weeks to design",null,null,"n1",2]
[null,"Step 2: Construction: Usually takes 2 to 4 weeks to complete",null,null,"n2",3]
[null,null,null,null,"Total Sample Points:"]
[]
[null,"List all sample points?"]
[]
[]
[null,null,null,null,null,null,null,"Variable of Interest and Relative Frequency"]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,"Goal:","P(<=4 weeks)"]
[]
[null,"Looking at the tree diagram it looks like 3 of the experimental outcomes match the 1 or fewer month requirement."]
[null,"But the manager does not think that each experimental outcome is equally likely. This is not a classical probability situation like flipping a coin or rolling dice."]
[null,"The manager thinks it would be best to look at past project records to determine probabilities."]
[null,"Past company records show this set of records for similar projects:",null,null,null,"Total Records = Total Sample Points:"]

{"sheet":"Retrofit (an)","index":16,"n_rows":60,"n_cols":10,"rows_kept":60,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Sound Home Earthquake Retrofitting",null,null,null,null,null,"Sample Points and Relative Frequency"]
[null,"Two steps for basic retrofit projects: Design and then Construction."]
[null,"Goal: The company needs to estimate the probability that it will take 1 month or less to complete a project.",null,null,null,null,null,"Sample Point","Frequency","% Frequency"]
[null,"Past company records show these possibilities:",null,null,null,null,null,"(1, 2)",6,0.2]
[null,"Step 1: Design. Usually it takes 1 or 2 weeks to design",null,null,"n1",2,null,"(1, 3)",12,0.4]
[null,"Step 2: Construction: Usually takes 2 to 4 weeks to complete",null,null,"n2",3,null,"(1, 4)",4,0.13333333333333333]
[null,null,null,null,"Total Sample Points:",{"$f":"F7*F6","v":6},null,"(2, 2)",2,6.6666666666666666E-2]
[null,null,null,null,null,null,null,"(2, 3)",5,0.16666666666666666]
[null,"List all sample points?",null,null,null,null,null,"(2, 4)",1,3.3333333333333333E-2]
[null,null,null,null,null,null,null,"Grand Total",30,1]
[]
[null,null,null,null,null,null,null,"Variable of Interest and Relative Frequency"]
[]
[null,null,null,null,null,null,null,"Total Weeks","Frequency","Probability"]
[null,null,null,null,null,null,null,3,6,0.2]
[null,null,null,null,null,null,null,4,14,0.46666666666666667]
[null,null,null,null,null,null,null,5,9,0.3]
[null,null,null,null,null,null,null,6,1,3.3333333333333333E-2]
[null,null,null,null,null,null,null,"Grand Total",30,1]
[]
[null,null,null,null,null,null,"Goal:","P(<=4 weeks)",{"$f":"SUM(J5:J6,J8)","v":0.66666666666666674},{"$f":"SUM(J16:J17)","v":0.66666666666666674}]
[]
[null,"Looking at the tree diagram it looks like 3 of the experimental outcomes match the 1 or fewer month requirement."]
[null,"But the manager does not think that each experimental outcome is equally likely. This is not a classical probability situation like flipping a coin or rolling dice."]
[null,"The manager thinks it would be best to look at past project records to determine probabilities."]
[null,"Past company records show this set of records for similar projects:",null,null,null,"Total Records = Total Sample Points:"]
[]
[]
[null,"Date","Project","Design time (weeks)","Construction time (weeks)","Sample Point","Total Weeks"]
[null,"2018-01-14","2752 SW Seola Lane ,98146",2,3,{"$f":"\"(\"&'Retrofit (an)'!$D31&\", \"&'Retrofit (an)'!$E31&\")\"","v":"(2, 3)"},{"$f":"SUM('Retrofit (an)'!$D31:$E31)","v":5}]
[null,"2018-02-08","2157 62nd Avenue S ,98118",1,2,{"$f":"\"(\"&'Retrofit (an)'!$D32&\", \"&'Retrofit (an)'!$E32&\")\"","v":"(1, 2)"},{"$f":"SUM('Retrofit (an)'!$D32:$E32)","v":3}]
[null,"2018-07-02","8682 NE 80th Street ,98115",1,2,{"$f":"\"(\"&'Retrofit (an)'!$D33&\", \"&'Retrofit (an)'!$E33&\")\"","v":"(1, 2)"},{"$f":"SUM('Retrofit (an)'!$D33:$E33)","v":3}]
[null,"2018-07-24","2274 S Mount Baker Circle ,98144",1,2,{"$f":"\"(\"&'Retrofit (an)'!$D34&\", \"&'Retrofit (an)'!$E34&\")\"","v":"(1, 2)"},{"$f":"SUM('Retrofit (an)'!$D34:$E34)","v":3}]
[null,"2018-08-26","362 E McGraw Street ,98112",1,4,{"$f":"\"(\"&'Retrofit (an)'!$D35&\", \"&'Retrofit (an)'!$E35&\")\"","v":"(1, 4)"},{"$f":"SUM('Retrofit (an)'!$D35:$E35)","v":5}]
[null,"2018-09-29","8354 NW 191st Lane ,98177",2,3,{"$f":"\"(\"&'Retrofit (an)'!$D36&\", \"&'Retrofit (an)'!$E36&\")\"","v":"(2, 3)"},{"$f":"SUM('Retrofit (an)'!$D36:$E36)","v":5}]
[null,"2018-11-10","2216 E Galer Street ,98112",1,3,{"$f":"\"(\"&'Retrofit (an)'!$D37&\", \"&'Retrofit (an)'!$E37&\")\"","v":"(1, 3)"},{"$f":"SUM('Retrofit (an)'!$D37:$E37)","v":4}]
[null,"2018-12-03","5232 Terry Avenue N ,98109",1,2,{"$f":"\"(\"&'Retrofit (an)'!$D38&\", \"&'Retrofit (an)'!$E38&\")\"","v":"(1, 2)"},{"$f":"SUM('Retrofit (an)'!$D38:$E38)","v":3}]
[null,"2019-01-22","8402 26th Ct S ,98168",1,3,{"$f":"\"(\"&'Retrofit (an)'!$D39&\", \"&'Retrofit (an)'!$E39&\")\"","v":"(1, 3)"},{"$f":"SUM('Retrofit (an)'!$D39:$E39)","v":4}]
[null,"2019-03-19","8223 Lewis Pl SW ,98116",2,2,{"$f":"\"(\"&'Retrofit (an)'!$D40&\", \"&'Retrofit (an)'!$E40&\")\"","v":"(2, 2)"},{"$f":"SUM('Retrofit (an)'!$D40:$E40)","v":4}]
[null,"2019-06-07","3749 Princeton Avenue NE ,98115",1,3,{"$f":"\"(\"&'Retrofit (an)'!$D41&\", \"&'Retrofit (an)'!$E41&\")\"","v":"(1, 3)"},{"$f":"SUM('Retrofit (an)'!$D41:$E41)","v":4}]
[null,"2019-06-19","6428 N 178th Lane ,98133",2,3,{"$f":"\"(\"&'Retrofit (an)'!$D42&\", \"&'Retrofit (an)'!$E42&\")\"","v":"(2, 3)"},{"$f":"SUM('Retrofit (an)'!$D42:$E42)","v":5}]
[null,"2019-11-08","5846 Rockery Drive S ,98118",1,3,{"$f":"\"(\"&'Retrofit (an)'!$D43&\", \"&'Retrofit (an)'!$E43&\")\"","v":"(1, 3)"},{"$f":"SUM('Retrofit (an)'!$D43:$E43)","v":4}]
[null,"2019-11-13","9739 SW Heinze Way ,98136",1,3,{"$f":"\"(\"&'Retrofit (an)'!$D44&\", \"&'Retrofit (an)'!$E44&\")\"","v":"(1, 3)"},{"$f":"SUM('Retrofit (an)'!$D44:$E44)","v":4}]
[null,"2020-01-25","4168 S 234th Street ,98198",1,3,{"$f":"\"(\"&'Retrofit (an)'!$D45&\", \"&'Retrofit (an)'!$E45&\")\"","v":"(1, 3)"},{"$f":"SUM('Retrofit (an)'!$D45:$E45)","v":4}]
[null,"2020-01-26","972 5th Pl S ,98168",1,2,{"$f":"\"(\"&'Retrofit (an)'!$D46&\", \"&'Retrofit (an)'!$E46&\")\"","v":"(1, 2)"},{"$f":"SUM('Retrofit (an)'!$D46:$E46)","v":3}]
[null,"2020-03-22","1203 7th Pl S ,98148",1,4,{"$f":"\"(\"&'Retrofit (an)'!$D47&\", \"&'Retrofit (an)'!$E47&\")\"","v":"(1, 4)"},{"$f":"SUM('Retrofit (an)'!$D47:$E47)","v":5}]
[null,"2020-04-06","7216 SW 102nd Lane ,98146",2,3,{"$f":"\"(\"&'Retrofit (an)'!$D48&\", \"&'Retrofit (an)'!$E48&\")\"","v":"(2, 3)"},{"$f":"SUM('Retrofit (an)'!$D48:$E48)","v":5}]
[null,"2020-05-13","3291 S Stevens Street ,98144",1,3,{"$f":"\"(\"&'Retrofit (an)'!$D49&\", \"&'Retrofit (an)'!$E49&\")\"","v":"(1, 3)"},{"$f":"SUM('Retrofit (an)'!$D49:$E49)","v":4}]
[null,"2020-06-10","3688 39th Avenue S ,98144",1,2,{"$f":"\"(\"&'Retrofit (an)'!$D50&\", \"&'Retrofit (an)'!$E50&\")\"","v":"(1, 2)"},{"$f":"SUM('Retrofit (an)'!$D50:$E50)","v":3}]
[null,"2020-06-16","9674 34th Lane S ,98188",2,4,{"$f":"\"(\"&'Retrofit (an)'!$D51&\", \"&'Retrofit (an)'!$E51&\")\"","v":"(2, 4)"},{"$f":"SUM('Retrofit (an)'!$D51:$E51)","v":6}]
[null,"2020-08-09","2542 1st Avenue SW ,98146",1,3,{"$f":"\"(\"&'Retrofit (an)'!$D52&\", \"&'Retrofit (an)'!$E52&\")\"","v":"(1, 3)"},{"$f":"SUM('Retrofit (an)'!$D52:$E52)","v":4}]
[null,"2020-09-07","7258 N 194th Street ,98133",2,3,{"$f":"\"(\"&'Retrofit (an)'!$D53&\", \"&'Retrofit (an)'!$E53&\")\"","v":"(2, 3)"},{"$f":"SUM('Retrofit (an)'!$D53:$E53)","v":5}]
[null,"2020-09-14","2573 W Cramer Street ,98199",1,4,{"$f":"\"(\"&'Retrofit (an)'!$D54&\", \"&'Retrofit (an)'!$E54&\")\"","v":"(1, 4)"},{"$f":"SUM('Retrofit (an)'!$D54:$E54)","v":5}]
[null,"2021-02-20","1540 Maiden Lane E ,98112",1,3,{"$f":"\"(\"&'Retrofit (an)'!$D55&\", \"&'Retrofit (an)'!$E55&\")\"","v":"(1, 3)"},{"$f":"SUM('Retrofit (an)'!$D55:$E55)","v":4}]
[null,"2021-03-07","3391 S 180th Place ,98188",1,3,{"$f":"\"(\"&'Retrofit (an)'!$D56&\", \"&'Retrofit (an)'!$E56&\")\"","v":"(1, 3)"},{"$f":"SUM('Retrofit (an)'!$D56:$E56)","v":4}]
[null,"2021-03-25","9172 64th Avenue SW ,98116",1,3,{"$f":"\"(\"&'Retrofit (an)'!$D57&\", \"&'Retrofit (an)'!$E57&\")\"","v":"(1, 3)"},{"$f":"SUM('Retrofit (an)'!$D57:$E57)","v":4}]
[null,"2021-05-01","5367 Meridian Ct N ,98133",1,4,{"$f":"\"(\"&'Retrofit (an)'!$D58&\", \"&'Retrofit (an)'!$E58&\")\"","v":"(1, 4)"},{"$f":"SUM('Retrofit (an)'!$D58:$E58)","v":5}]
[null,"2021-05-18","2220 N 102nd Street ,98133",1,3,{"$f":"\"(\"&'Retrofit (an)'!$D59&\", \"&'Retrofit (an)'!$E59&\")\"","v":"(1, 3)"},{"$f":"SUM('Retrofit (an)'!$D59:$E59)","v":4}]
[null,"2021-08-31","5597 32nd Avenue ,98122",2,2,{"$f":"\"(\"&'Retrofit (an)'!$D60&\", \"&'Retrofit (an)'!$E60&\")\"","v":"(2, 2)"},{"$f":"SUM('Retrofit (an)'!$D60:$E60)","v":4}]

{"sheet":"V(17)","index":17,"n_rows":97,"n_cols":18,"rows_kept":97,"cut":false,"hidden":false,"merged":[[43,5,44,9],[77,5,78,7],[89,5,90,7],[96,5,97,7]]}
[]
[null,"Logical Tests Used for Counting Sample Points",null,null,null,null,"Name","HairColor","EyeColor"]
[null,null,null,null,null,null,"Sioux","Brown","Hazel"]
[null,"Event Black Hair",null,null,null,null,"Chin","Black","Blue"]
[null,null,null,null,null,null,"Shelia","Black","Brown"]
[null,null,null,null,null,null,"Gigi","Brown","Hazel"]
[null,null,null,null,null,null,"Tyrone","Black","Brown"]
[null,null,null,null,null,null,"Lin","Blond","Brown"]
[null,null,null,null,null,null,"Ducky","Brown","Brown"]
[null,null,null,null,null,null,"Kip","Brown","Hazel"]
[null,"Event Brown Hair",null,null,null,null,"Linda","Red","Blue"]
[null,null,null,null,null,null,"Jo","Pink","Green"]
[null,null,null,null,null,null,"Total Records:"]
[]
[null,null,null,null,null,"1) Single Condition Logical Test: Equal to Brown Hair"]
[null,null,null,null,null,"Condition","Brown"]
[null,null,null,null,null,"Count",null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G17),\"\")","v":""}]
[]
[null,"Event NOT Brown Hair",null,null,null,{"$f":"\"P(\"&G16&\")\"","v":"P(Brown)"},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G19),\"\")","v":""}]
[null,null,null,null,null,"2) Not Logical Test: NOT Brown Hair"]
[null,null,null,null,null,"Condition",{"$f":"G16","v":"Brown"}]
[null,null,null,null,null,"Count",null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G22),\"\")","v":""}]
[]
[null,null,null,null,null,{"$f":"\"P(NOT \"&LEFT($G$16,2)&\".)\"","v":"P(NOT Br.)"},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G24),\"\")","v":""}]
[null,null,null,null,null,"Complement Rule: If P(B), then P(Not B) = 1 - P(B)"]
[null,null,null,null,null,{"$f":"\"P(NOT \"&LEFT($G$16,2)&\".)\"","v":"P(NOT Br.)"},null,{"$f":"IF(ISBLANK(G26),\"\",\" 1-\"&G19)","v":""}]
[null,"Event Brown Hair OR Black Hair"]
[null,null,null,null,null,"3a) OR Logical Test for Mutually Exclusive Events (One Column):"]
[null,null,null,null,null,"Brown Hair OR Black Hair",null,null,null,null,null,null,null,null,null,"Best version if you have many OR conditions:"]
[null,null,null,null,null,"Condition","Brown",null,null,null,null,"Name","Hair Color","Eye Color",null,"Alternatives:"]
[null,null,null,null,null,"Condition","Black",null,null,null,null,"Sioux","Brown","Hazel",null,"Brown Hair OR Hazel Eyes"]
[null,null,null,null,null,"Count",null,null,null,null,null,"Chin","Black","Blue",null,"Condition","Brown","Hair"]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G32),\"\")","v":""},null,null,null,null,null,"Shelia","Black","Brown",null,"Condition","Hazel","Eyes"]
[null,null,null,null,null,"Count",null,null,null,null,null,"Gigi","Brown","Hazel",null,"Count",{"$f":"ROWS(_xlfn._xlws.FILTER(M31:M40,ISNUMBER(_xlfn.XMATCH(M31:M40,Q32:Q33))))","v":4}]
[null,"Event Brown Hair OR Hazel Eyes",null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G34),\"\")","v":""},null,null,null,null,null,"Tyrone","Black","Brown",null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(Q34),\"\")","v":"=ROWS(FILTER(M31:M40,ISNUMBER(XMATCH(M31:M40,Q32:Q33))))"}]
[null,null,null,null,null,null,null,null,null,null,null,"Lin","Blond","Brown"]
[null,null,null,null,null,"3b) OR Logical Test for Events that are not Mutually Exclusive",null,null,null,null,null,"Ducky","Brown","Brown",null,"Alternatives:"]
[null,null,null,null,null,"Brown Hair OR Hazel Eyes",null,null,"(Two Columns):",null,null,"Kip","Brown","Hazel",null,"Brown Hair OR Hazel Eyes"]
[null,null,null,null,null,"Condition","Brown","Hair",null,null,null,"Linda","Red","Blue",null,"Condition","Brown","Hair"]
[null,null,null,null,null,"Condition","Hazel","Eyes",null,null,null,"Jo","Pink","Green",null,"Condition","Hazel","Eyes"]
[null,null,null,null,null,"Count",null,null,null,null,null,"Total Records:",null,{"$f":"ROWS(L31:N40)","v":10},null,"Count",{"$f":"SUM(--((M31:M40=G39)+(N31:N40=G40)>0))","v":4}]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G41),\"\")","v":""},null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(Q41),\"\")","v":"=SUM(--((M31:M40=G39)+(N31:N40=G40)>0))"}]
[null,"Event Brown Hair AND Hazel Eyes",null,null,null,"Count"]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G43),\"\")","v":""},null,null,null,null,null,null,null,null,null,"Alternatives:"]
[null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G46),\"\")","v":""},null,null,null,null,null,null,null,null,null,null,"Brown Hair OR Hazel Eyes"]
[null,null,null,null,null,"4) AND Logical Test: Brown Hair AND Hazel Eyes",null,null,null,null,null,null,null,null,null,"Condition","Brown","Hair"]
[null,null,null,null,null,"Condition","Brown","Hair",null,null,null,null,null,null,null,"Condition","Hazel","Eyes"]
[null,null,null,null,null,"Condition","Hazel","Eyes",null,null,null,null,null,null,null,"Count",{"$f":"SUM(IF((M31:M40=G39)+(N31:N40=G40),1))","v":4}]
[null,null,null,null,null,"Count",null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(Q48),\"\")","v":"=SUM(IF((M31:M40=G39)+(N31:N40=G40),1))"}]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G49),\"\")","v":""}]
[]
[]
[null,"Logical Tests Used for Filtering Sample Points",null,null,null,null,"Name","HairColor","EyeColor"]
[null,"We can use the FILTER array function to filter a data set",null,null,null,null,"Sioux","Brown","Hazel"]
[null,"in order to see specified sample points.",null,null,null,null,"Chin","Black","Blue"]
[null,null,null,null,null,null,"Shelia","Black","Brown"]
[null,"FILTER(ArrayToFilter,LogicalTestArray)",null,null,null,null,"Gigi","Brown","Hazel"]
[null,"ArrayToFilter & LogicalTestArray must be same size.",null,null,null,null,"Tyrone","Black","Brown"]
[null,"OR Logical Test uses + in direct array operation.",null,null,null,null,"Lin","Blond","Brown"]
[null,"AND Logical Test uses * in direct array operation.",null,null,null,null,"Ducky","Brown","Brown"]
[null,"TRUE or any non-zero number = TRUE.",null,null,null,null,"Kip","Brown","Hazel"]
[null,"FALSE or 0 = FALSE.",null,null,null,null,"Linda","Red","Blue"]
[null,null,null,null,null,null,"Jo","Pink","Green"]
[null,null,null,null,null,null,"Total Records:"]
[null,"Event Brown Hair"]
[null,null,null,null,null,"1) Single Condition Logical Test: Equal to Brown Hair"]
[null,null,null,null,null,"Condition","Brown","Matching Rows:"]
[]
[null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(I68),\"\")","v":""}]
[]
[]
[]
[null,"Event Brown Hair OR Black Hair",null,null,null,"3a) OR Logical Test for Mutually Exclusive Events (One Column):"]
[null,null,null,null,null,"Brown Hair OR Black Hair"]
[null,null,null,null,null,"Condition","Brown","Matching Rows:"]
[null,null,null,null,null,"Condition","Black"]
[]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(I76),\"\")","v":""}]
[]
[]
[null,"Event Brown Hair OR Hazel Eyes"]
[]
[]
[null,null,null,null,null,"3b) OR Logical Test for Events that are not Mutually Exclusive"]
[null,null,null,null,null,null,null,null,"(Two Columns):"]
[null,null,null,null,null,"Brown Hair OR Hazel Eyes"]
[null,null,null,null,null,"Condition","Brown","Hair","Matching Rows:"]
[null,null,null,null,null,"Condition","Hazel","Eyes"]
[]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(I88),\"\")","v":""}]
[]
[]
[null,null,null,null,null,"4) AND Logical Test: Brown Hair AND Hazel Eyes"]
[null,"Event Brown Hair AND Hazel Eyes",null,null,null,"Condition","Brown","Hair","Matching Rows:"]
[null,null,null,null,null,"Condition","Hazel","Eyes"]
[null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G98),\"\")","v":""}]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(I95),\"\")","v":""}]

{"sheet":"V(17an)","index":18,"n_rows":97,"n_cols":18,"rows_kept":97,"cut":false,"hidden":false,"merged":[[43,5,44,9],[77,5,78,7],[89,5,90,7],[96,5,97,7]]}
[]
[null,"Logical Tests Used for Counting Sample Points",null,null,null,null,"Name","HairColor","EyeColor"]
[null,null,null,null,null,null,"Sioux","Brown","Hazel"]
[null,"Event Black Hair",null,null,null,null,"Chin","Black","Blue"]
[null,null,null,null,null,null,"Shelia","Black","Brown"]
[null,null,null,null,null,null,"Gigi","Brown","Hazel"]
[null,null,null,null,null,null,"Tyrone","Black","Brown"]
[null,null,null,null,null,null,"Lin","Blond","Brown"]
[null,null,null,null,null,null,"Ducky","Brown","Brown"]
[null,null,null,null,null,null,"Kip","Brown","Hazel"]
[null,"Event Brown Hair",null,null,null,null,"Linda","Red","Blue"]
[null,null,null,null,null,null,"Jo","Pink","Green"]
[null,null,null,null,null,null,"Total Records:",null,{"$f":"ROWS(G3:I12)","v":10}]
[]
[null,null,null,null,null,"1) Single Condition Logical Test: Equal to Brown Hair"]
[null,null,null,null,null,"Condition","Brown"]
[null,null,null,null,null,"Count",{"$f":"COUNTIFS(H3:H12,G16)","v":4},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G17),\"\")","v":"=COUNTIFS(H3:H12,G16)"}]
[]
[null,"Event NOT Brown Hair",null,null,null,{"$f":"\"P(\"&G16&\")\"","v":"P(Brown)"},{"$f":"G17/I13","v":0.4},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G19),\"\")","v":"=G17/I13"}]
[null,null,null,null,null,"2) Not Logical Test: NOT Brown Hair"]
[null,null,null,null,null,"Condition",{"$f":"G16","v":"Brown"}]
[null,null,null,null,null,"Count",{"$f":"COUNTIFS(H3:H12,\"<>\"&G21)","v":6},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G22),\"\")","v":"=COUNTIFS(H3:H12,\"<>\"&G21)"}]
[]
[null,null,null,null,null,{"$f":"\"P(NOT \"&LEFT($G$16,2)&\".)\"","v":"P(NOT Br.)"},{"$f":"G22/I13","v":0.6},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G24),\"\")","v":"=G22/I13"}]
[null,null,null,null,null,"Complement Rule: If P(B), then P(Not B) = 1 - P(B)"]
[null,null,null,null,null,{"$f":"\"P(NOT \"&LEFT($G$16,2)&\".)\"","v":"P(NOT Br.)"},{"$f":"1-G19","v":0.6},{"$f":"IF(ISBLANK(G26),\"\",\" 1-\"&G19)","v":" 1-0.4"}]
[null,"Event Brown Hair OR Black Hair"]
[null,null,null,null,null,"3a) OR Logical Test for Mutually Exclusive Events (One Column):"]
[null,null,null,null,null,"Brown Hair OR Black Hair",null,null,null,null,null,null,null,null,null,"Best version if you have many OR conditions:"]
[null,null,null,null,null,"Condition","Brown",null,null,null,null,"Name","Hair Color","Eye Color",null,"Alternatives:"]
[null,null,null,null,null,"Condition","Black",null,null,null,null,"Sioux","Brown","Hazel",null,"Brown Hair OR Hazel Eyes"]
[null,null,null,null,null,"Count",{"$f":"ROWS(_xlfn._xlws.FILTER(M31:M40,(M31:M40=G30)+(M31:M40=G31)))","v":7},null,null,null,null,"Chin","Black","Blue",null,"Condition","Brown","Hair"]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G32),\"\")","v":"=ROWS(FILTER(M31:M40,(M31:M40=G30)+(M31:M40=G31)))"},null,null,null,null,null,"Shelia","Black","Brown",null,"Condition","Hazel","Eyes"]
[null,null,null,null,null,"Count",{"$f":"COUNTIFS(M31:M40,G30)+COUNTIFS(M31:M40,G31)","v":7},null,null,null,null,"Gigi","Brown","Hazel",null,"Count",{"$f":"ROWS(_xlfn._xlws.FILTER(M31:M40,ISNUMBER(_xlfn.XMATCH(M31:M40,Q32:Q33))))","v":4}]
[null,"Event Brown Hair OR Hazel Eyes",null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G34),\"\")","v":"=COUNTIFS(M31:M40,G30)+COUNTIFS(M31:M40,G31)"},null,null,null,null,null,"Tyrone","Black","Brown",null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(Q34),\"\")","v":"=ROWS(FILTER(M31:M40,ISNUMBER(XMATCH(M31:M40,Q32:Q33))))"}]
[null,null,null,null,null,null,null,null,null,null,null,"Lin","Blond","Brown"]
[null,null,null,null,null,"3b) OR Logical Test for Events that are not Mutually Exclusive",null,null,null,null,null,"Ducky","Brown","Brown",null,"Alternatives:"]
[null,null,null,null,null,"Brown Hair OR Hazel Eyes",null,null,"(Two Columns):",null,null,"Kip","Brown","Hazel",null,"Brown Hair OR Hazel Eyes"]
[null,null,null,null,null,"Condition","Brown","Hair",null,null,null,"Linda","Red","Blue",null,"Condition","Brown","Hair"]
[null,null,null,null,null,"Condition","Hazel","Eyes",null,null,null,"Jo","Pink","Green",null,"Condition","Hazel","Eyes"]
[null,null,null,null,null,"Count",{"$f":"ROWS(_xlfn._xlws.FILTER(M31:N40,(M31:M40=G39)+(N31:N40=G40)))","v":4},null,null,null,null,"Total Records:",null,{"$f":"ROWS(L31:N40)","v":10},null,"Count",{"$f":"SUM(--((M31:M40=G39)+(N31:N40=G40)>0))","v":4}]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G41),\"\")","v":"=ROWS(FILTER(M31:N40,(M31:M40=G39)+(N31:N40=G40)))"},null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(Q41),\"\")","v":"=SUM(--((M31:M40=G39)+(N31:N40=G40)>0))"}]
[null,"Event Brown Hair AND Hazel Eyes",null,null,null,"Count",{"$f":"COUNTIFS(M31:M40,G39)+COUNTIFS(N31:N40,G40)-COUNTIFS(M31:M40,G39,N31:N40,G40)","v":4}]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G43),\"\")","v":"=COUNTIFS(M31:M40,G39)+COUNTIFS(N31:N40,G40)-COUNTIFS(M31:M40,G39,N31:N40,G40)"},null,null,null,null,null,null,null,null,null,"Alternatives:"]
[null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G46),\"\")","v":""},null,null,null,null,null,null,null,null,null,null,"Brown Hair OR Hazel Eyes"]
[null,null,null,null,null,"4) AND Logical Test: Brown Hair AND Hazel Eyes",null,null,null,null,null,null,null,null,null,"Condition","Brown","Hair"]
[null,null,null,null,null,"Condition","Brown","Hair",null,null,null,null,null,null,null,"Condition","Hazel","Eyes"]
[null,null,null,null,null,"Condition","Hazel","Eyes",null,null,null,null,null,null,null,"Count",{"$f":"SUM(IF((M31:M40=G39)+(N31:N40=G40),1))","v":4}]
[null,null,null,null,null,"Count",{"$f":"COUNTIFS(M31:M40,G47,N31:N40,G48)","v":3},null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(Q48),\"\")","v":"=SUM(IF((M31:M40=G39)+(N31:N40=G40),1))"}]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G49),\"\")","v":"=COUNTIFS(M31:M40,G47,N31:N40,G48)"}]
[]
[]
[null,"Logical Tests Used for Filtering Sample Points",null,null,null,null,"Name","HairColor","EyeColor"]
[null,"We can use the FILTER array function to filter a data set",null,null,null,null,"Sioux","Brown","Hazel"]
[null,"in order to see specified sample points.",null,null,null,null,"Chin","Black","Blue"]
[null,null,null,null,null,null,"Shelia","Black","Brown"]
[null,"FILTER(ArrayToFilter,LogicalTestArray)",null,null,null,null,"Gigi","Brown","Hazel"]
[null,"ArrayToFilter & LogicalTestArray must be same size.",null,null,null,null,"Tyrone","Black","Brown"]
[null,"OR Logical Test uses + in direct array operation.",null,null,null,null,"Lin","Blond","Brown"]
[null,"AND Logical Test uses * in direct array operation.",null,null,null,null,"Ducky","Brown","Brown"]
[null,"TRUE or any non-zero number = TRUE.",null,null,null,null,"Kip","Brown","Hazel"]
[null,"FALSE or 0 = FALSE.",null,null,null,null,"Linda","Red","Blue"]
[null,null,null,null,null,null,"Jo","Pink","Green"]
[null,null,null,null,null,null,"Total Records:",null,{"$f":"ROWS(G54:I63)","v":10}]
[null,"Event Brown Hair"]
[null,null,null,null,null,"1) Single Condition Logical Test: Equal to Brown Hair"]
[null,null,null,null,null,"Condition","Brown","Matching Rows:"]
[null,null,null,null,null,null,null,null,{"$f":"_xlfn._xlws.FILTER(H54:H63,H54:H63=G67,\"NA\")","v":"Brown"}]
[null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(I68),\"\")","v":"=FILTER(H54:H63,H54:H63=G67,\"NA\")"},null,null,null,"Brown"]
[null,null,null,null,null,null,null,null,"Brown"]
[null,null,null,null,null,null,null,null,"Brown"]
[]
[null,"Event Brown Hair OR Black Hair",null,null,null,"3a) OR Logical Test for Mutually Exclusive Events (One Column):"]
[null,null,null,null,null,"Brown Hair OR Black Hair"]
[null,null,null,null,null,"Condition","Brown","Matching Rows:"]
[null,null,null,null,null,"Condition","Black",null,{"$f":"_xlfn._xlws.FILTER(H54:H63,(H54:H63=G75)+(H54:H63=G76))","v":"Brown"}]
[null,null,null,null,null,null,null,null,"Black"]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(I76),\"\")","v":"=FILTER(H54:H63,(H54:H63=G75)+(H54:H63=G76))"},null,null,"Black"]
[null,null,null,null,null,null,null,null,"Brown"]
[null,null,null,null,null,null,null,null,"Black"]
[null,"Event Brown Hair OR Hazel Eyes",null,null,null,null,null,null,"Brown"]
[null,null,null,null,null,null,null,null,"Brown"]
[]
[null,null,null,null,null,"3b) OR Logical Test for Events that are not Mutually Exclusive"]
[null,null,null,null,null,null,null,null,"(Two Columns):"]
[null,null,null,null,null,"Brown Hair OR Hazel Eyes"]
[null,null,null,null,null,"Condition","Brown","Hair","Matching Rows:"]
[null,null,null,null,null,"Condition","Hazel","Eyes",{"$f":"_xlfn._xlws.FILTER(H54:I63,(H54:H63=G87)+(I54:I63=G88))","v":"Brown"},"Hazel"]
[null,null,null,null,null,null,null,null,"Brown","Hazel"]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(I88),\"\")","v":"=FILTER(H54:I63,(H54:H63=G87)+(I54:I63=G88))"},null,null,"Brown","Brown"]
[null,null,null,null,null,null,null,null,"Brown","Hazel"]
[]
[null,null,null,null,null,"4) AND Logical Test: Brown Hair AND Hazel Eyes"]
[null,"Event Brown Hair AND Hazel Eyes",null,null,null,"Condition","Brown","Hair","Matching Rows:"]
[null,null,null,null,null,"Condition","Hazel","Eyes",{"$f":"_xlfn._xlws.FILTER(H54:I63,(H54:H63=G87)*(I54:I63=G88))","v":"Brown"},"Hazel"]
[null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G98),\"\")","v":""},null,null,null,"Brown","Hazel"]
[null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(I95),\"\")","v":"=FILTER(H54:I63,(H54:H63=G87)*(I54:I63=G88))"},null,null,"Brown","Hazel"]

{"sheet":"V(18)","index":19,"n_rows":45,"n_cols":10,"rows_kept":45,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Using the Addition Law of Probability"]
[null,"Mutually Exclusive Events: P(A OR B) = P(A) + P(B)."]
[null,"Events that are NOT Mutually Exclusive: P(A OR B) = P(A) + P(B) - P(A AND B)."]
[null,null,null,null,null,null,null,null,"SN","PPM"]
[null,"4 examples of calculating the probability for an OR Logical Test:",null,null,null,null,null,null,"Space","Pike's"]
[null,"1) From Data Set",null,null,null,null,null,"Visitor","Needle","Place Market"]
[null,"2) From Frequency Distribution",null,null,null,null,null,1,"Yes","Yes"]
[null,"3) From Cross Tabulated Report",null,null,null,null,null,2,"No","Yes"]
[null,"4) From Pre-determined Probabilities",null,null,null,null,null,3,"No","Yes"]
[null,null,null,null,null,null,null,4,"No","No"]
[null,"1) From Data Set for visitors to Seattle",null,null,null,null,null,5,"Yes","Yes"]
[null,"For a randomly selected Seattle visitor calculate the probability",null,null,null,null,null,6,"Yes","Yes"]
[null,"that they visited the SN or PPM.",null,null,null,null,null,7,"No","No"]
[null,null,"Condition","Yes","from Space Needle field",null,null,8,"Yes","No"]
[null,null,"Count",null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D16),\"\")","v":""},null,null,9,"No","Yes"]
[null,null,"Condition","Yes","from Pike's Place field",null,null,10,"Yes","Yes"]
[null,null,"Count",null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D18),\"\")","v":""},null,null,"Total Records",null,{"$f":"ROWS(PPM)","v":10}]
[null,null,"Condition","Yes","Visited both sites (AND)"]
[null,null,"Count",null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D20),\"\")","v":""}]
[null,"P(SN OR PPM)",null,null,{"$f":"IF(ISBLANK(D21),\"\",\" (\"&D16&\"+\"&D18&\"-\"&D20&\")/\"&J18)","v":""}]
[null,"P(SN OR PPM)",null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D22),\"\")","v":""}]
[]
[null,"2) From Frequency Distribution with Mutually Exclusive Categories",null,null,null,null,null,null,"Arrival","Frequency"]
[null,"For a randomly selected Delta Airline Passenger calculate the",null,null,null,null,null,null,"Early",100]
[null,"following probabilities:",null,null,null,null,null,null,"On Time",794]
[null,"P(Early OR On Time)",null,null,{"$f":"IF(ISBLANK(D27),\"\",\" (\"&J25&\"+\"&J26&\")/\"&J29)","v":""},null,null,null,"Late",81]
[null,"P(Cancelled)",null,null,{"$f":"IF(ISBLANK(D28),\"\",\" \"&J28&\"/\"&J29)","v":""},null,null,null,"Canceled",25]
[null,"P(Not Cancelled)",null,null,{"$f":"IF(ISBLANK(D29),\"\",\" 1-\"&D28)","v":""},null,null,null,"Grand Total",1000]
[]
[null,"3) From Cross Tabulated Report created from the visitors to Seattle data set "]
[null,"For a randomly selected Seattle visitor calculate the probability"]
[null,"that they visited the SN or PPM.",null,null,null,null,"Frequency","Pike's Place M."]
[null,null,null,null,null,null,"Space N.",{"$f":"TRANSPOSE(_xlfn._xlws.SORT(_xlfn.UNIQUE(J8:J17)))","v":"No"},"Yes","Totals"]
[null,"P(SN OR PPM)",null,null,null,null,{"$f":"_xlfn._xlws.SORT(_xlfn.UNIQUE(I8:I17))","v":"No"},{"$f":"COUNTIFS(I8:I17,G35:G36,J8:J17,H34:I34)","v":2},3,{"$f":"SUM(H35:I35)","v":5}]
[null,null,null,{"$f":"IF(ISBLANK(D35),\"\",\" (\"&J36&\"+\"&I37&\"-\"&I36&\")/\"&J37)","v":""},null,null,"Yes",1,4,{"$f":"SUM(H36:I36)","v":5}]
[null,null,null,null,null,null,"Totals",{"$f":"SUM(H35:H36)","v":3},{"$f":"SUM(I35:I36)","v":7},{"$f":"SUM(H37:I37)","v":10}]
[null,"4) From Pre-determined Probabilities"]
[null,"For a randomly selected Seattle visitor calculate the probability"]
[null,"that they visited the SN or PPM."]
[null,"P(SN)",null,0.5]
[null,"P(PPM)",null,0.7]
[null,"P(SS AND PPM)",null,0.4]
[null,"P(SN OR PPM)",null,null,null,{"$f":"IF(ISBLANK(E44),\"\",\" \"&D41&\"+\"&D42&\"-\"&D43)","v":""}]
[null,"OR might be shown as: P(At least 1 site), or, P(1 or more sites)"]

{"sheet":"V(18an)","index":20,"n_rows":45,"n_cols":10,"rows_kept":45,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Using the Addition Law of Probability"]
[null,"Mutually Exclusive Events: P(A OR B) = P(A) + P(B)."]
[null,"Events that are NOT Mutually Exclusive: P(A OR B) = P(A) + P(B) - P(A AND B)."]
[null,null,null,null,null,null,null,null,"SN","PPM"]
[null,"4 examples of calculating the probability for an OR Logical Test:",null,null,null,null,null,null,"Space","Pike's"]
[null,"1) From Data Set",null,null,null,null,null,"Visitor","Needle","Place Market"]
[null,"2) From Frequency Distribution",null,null,null,null,null,1,"Yes","Yes"]
[null,"3) From Cross Tabulated Report",null,null,null,null,null,2,"No","Yes"]
[null,"4) From Pre-determined Probabilities",null,null,null,null,null,3,"No","Yes"]
[null,null,null,null,null,null,null,4,"No","No"]
[null,"1) From Data Set for visitors to Seattle",null,null,null,null,null,5,"Yes","Yes"]
[null,"For a randomly selected Seattle visitor calculate the probability",null,null,null,null,null,6,"Yes","Yes"]
[null,"that they visited the SN or PPM.",null,null,null,null,null,7,"No","No"]
[null,null,"Condition","Yes","from Space Needle field",null,null,8,"Yes","No"]
[null,null,"Count",{"$f":"COUNTIFS(I8:I17,D15)","v":5},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D16),\"\")","v":"=COUNTIFS(I8:I17,D15)"},null,null,9,"No","Yes"]
[null,null,"Condition","Yes","from Pike's Place field",null,null,10,"Yes","Yes"]
[null,null,"Count",{"$f":"COUNTIFS(J8:J17,D17)","v":7},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D18),\"\")","v":"=COUNTIFS(J8:J17,D17)"},null,null,"Total Records",null,{"$f":"ROWS(PPM)","v":10}]
[null,null,"Condition","Yes","Visited both sites (AND)"]
[null,null,"Count",{"$f":"COUNTIFS(I8:I17,D19,J8:J17,D19)","v":4},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D20),\"\")","v":"=COUNTIFS(I8:I17,D19,J8:J17,D19)"}]
[null,"P(SN OR PPM)",null,{"$f":"(D16+D18-D20)/J18","v":0.8},{"$f":"IF(ISBLANK(D21),\"\",\" (\"&D16&\"+\"&D18&\"-\"&D20&\")/\"&J18)","v":" (5+7-4)/10"}]
[null,"P(SN OR PPM)",null,{"$f":"ROWS(_xlfn._xlws.FILTER(H8:H17,(I8:I17=D19)+(J8:J17=D19)))/J18","v":0.8},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D22),\"\")","v":"=ROWS(FILTER(H8:H17,(I8:I17=D19)+(J8:J17=D19)))/J18"}]
[]
[null,"2) From Frequency Distribution with Mutually Exclusive Categories",null,null,null,null,null,null,"Arrival","Frequency"]
[null,"For a randomly selected Delta Airline Passenger calculate the",null,null,null,null,null,null,"Early",100]
[null,"following probabilities:",null,null,null,null,null,null,"On Time",794]
[null,"P(Early OR On Time)",null,{"$f":"(J25+J26)/J29","v":0.89400000000000002},{"$f":"IF(ISBLANK(D27),\"\",\" (\"&J25&\"+\"&J26&\")/\"&J29)","v":" (100+794)/1000"},null,null,null,"Late",81]
[null,"P(Cancelled)",null,{"$f":"J28/J29","v":2.5000000000000001E-2},{"$f":"IF(ISBLANK(D28),\"\",\" \"&J28&\"/\"&J29)","v":" 25/1000"},null,null,null,"Canceled",25]
[null,"P(Not Cancelled)",null,{"$f":"1-D28","v":0.97499999999999998},{"$f":"IF(ISBLANK(D29),\"\",\" 1-\"&D28)","v":" 1-0.025"},null,null,null,"Grand Total",1000]
[]
[null,"3) From Cross Tabulated Report created from the visitors to Seattle data set "]
[null,"For a randomly selected Seattle visitor calculate the probability"]
[null,"that they visited the SN or PPM.",null,null,null,null,"Frequency","Pike's Place M."]
[null,null,null,null,null,null,"Space N.",{"$f":"TRANSPOSE(_xlfn._xlws.SORT(_xlfn.UNIQUE(J8:J17)))","v":"No"},"Yes","Totals"]
[null,"P(SN OR PPM)",null,{"$f":"(J36+I37-I36)/J37","v":0.8},null,null,{"$f":"_xlfn._xlws.SORT(_xlfn.UNIQUE(I8:I17))","v":"No"},{"$f":"COUNTIFS(I8:I17,G35:G36,J8:J17,H34:I34)","v":2},3,{"$f":"SUM(H35:I35)","v":5}]
[null,null,null,{"$f":"IF(ISBLANK(D35),\"\",\" (\"&J36&\"+\"&I37&\"-\"&I36&\")/\"&J37)","v":" (5+7-4)/10"},null,null,"Yes",1,4,{"$f":"SUM(H36:I36)","v":5}]
[null,null,null,null,null,null,"Totals",{"$f":"SUM(H35:H36)","v":3},{"$f":"SUM(I35:I36)","v":7},{"$f":"SUM(H37:I37)","v":10}]
[null,"4) From Pre-determined Probabilities"]
[null,"For a randomly selected Seattle visitor calculate the probability"]
[null,"that they visited the SN or PPM."]
[null,"P(SN)",null,0.5]
[null,"P(PPM)",null,0.7]
[null,"P(SS AND PPM)",null,0.4]
[null,"P(SN OR PPM)",null,null,{"$f":"D41+D42-D43","v":0.79999999999999993},{"$f":"IF(ISBLANK(E44),\"\",\" \"&D41&\"+\"&D42&\"-\"&D43)","v":" 0.5+0.7-0.4"}]
[null,"OR might be shown as: P(At least 1 site), or, P(1 or more sites)"]

{"sheet":"Seattle(1)","index":21,"n_rows":204,"n_cols":41,"rows_kept":204,"cut":false,"hidden":false,"merged":[]}
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Creat Table:"]
[null,"Travel survey of people who visit Seattle"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor","Visit Space Needle?","Visit Pike's Place Market?","Visit Alki Beach?"]
[null,"Visitor","Visit Space Needle?","Visit Pike's Place Market?",null,null,null,null,null,null,null,"P(Space Needle)",null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(M4),\"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"Visitor \"&_xlfn.SEQUENCE(200)","v":"Visitor 1"},{"$f":"IF(_xlfn.SEQUENCE(200)<=45+45,\"Yes\",\"No\")","v":"Yes"},{"$f":"IF(_xlfn.SEQUENCE(200)<=65+65,\"Yes\",\"No\")","v":"Yes"},{"$f":"IF(_xlfn.SEQUENCE(200)<=25+35,\"Yes\",\"No\")","v":"Yes"}]
[null,"Visitor 1","Yes","Yes",null,null,null,null,null,null,null,"P(Pike's Place Market)",null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(M5),\"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 2","Yes","Yes","Yes"]
[null,"Visitor 2","No","No",null,null,null,null,null,null,null,"P(Space Needle AND Pike's Place Market)",null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(M6),\"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 3","Yes","Yes","Yes"]
[null,"Visitor 3","Yes","Yes",null,null,null,null,null,null,null,"P(Space Needle OR Pike's Place Market)",null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(M7),\"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 4","Yes","Yes","Yes"]
[null,"Visitor 4","Yes","Yes",null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(H8),\"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 5","Yes","Yes","Yes"]
[null,"Visitor 5","Yes","Yes",null,null,null,null,null,null,null,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 6","Yes","Yes","Yes"]
[null,"Visitor 6","Yes","No",null,null,null,null,null,null,null,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 7","Yes","Yes","Yes"]
[null,"Visitor 7","No","Yes",null,null,null,null,null,null,null,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 8","Yes","Yes","Yes"]
[null,"Visitor 8","Yes","Yes",null,null,null,null,null,null,null,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 9","Yes","Yes","Yes"]
[null,"Visitor 9","Yes","Yes",null,null,null,null,null,null,null,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 10","Yes","Yes","Yes"]
[null,"Visitor 10","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 11","Yes","Yes","Yes"]
[null,"Visitor 11","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 12","Yes","Yes","Yes"]
[null,"Visitor 12","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 13","Yes","Yes","Yes"]
[null,"Visitor 13","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 14","Yes","Yes","Yes"]
[null,"Visitor 14","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 15","Yes","Yes","Yes"]
[null,"Visitor 15","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 16","Yes","Yes","Yes"]
[null,"Visitor 16","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 17","Yes","Yes","Yes"]
[null,"Visitor 17","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 18","Yes","Yes","Yes"]
[null,"Visitor 18","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 19","Yes","Yes","Yes"]
[null,"Visitor 19","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 20","Yes","Yes","Yes"]
[null,"Visitor 20","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 21","Yes","Yes","Yes"]
[null,"Visitor 21","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 22","Yes","Yes","Yes"]
[null,"Visitor 22","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 23","Yes","Yes","Yes"]
[null,"Visitor 23","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 24","Yes","Yes","Yes"]
[null,"Visitor 24","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 25","Yes","Yes","Yes"]
[null,"Visitor 25","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 26","Yes","Yes","Yes"]
[null,"Visitor 26","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 27","Yes","Yes","Yes"]
[null,"Visitor 27","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 28","Yes","Yes","Yes"]
[null,"Visitor 28","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 29","Yes","Yes","Yes"]
[null,"Visitor 29","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 30","Yes","Yes","Yes"]
[null,"Visitor 30","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 31","Yes","Yes","Yes"]
[null,"Visitor 31","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 32","Yes","Yes","Yes"]
[null,"Visitor 32","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 33","Yes","Yes","Yes"]
[null,"Visitor 33","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 34","Yes","Yes","Yes"]
[null,"Visitor 34","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 35","Yes","Yes","Yes"]
[null,"Visitor 35","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 36","Yes","Yes","Yes"]
[null,"Visitor 36","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 37","Yes","Yes","Yes"]
[null,"Visitor 37","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 38","Yes","Yes","Yes"]
[null,"Visitor 38","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 39","Yes","Yes","Yes"]
[null,"Visitor 39","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 40","Yes","Yes","Yes"]
[null,"Visitor 40","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 41","Yes","Yes","Yes"]
[null,"Visitor 41","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 42","Yes","Yes","Yes"]
[null,"Visitor 42","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 43","Yes","Yes","Yes"]
[null,"Visitor 43","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 44","Yes","Yes","Yes"]
[null,"Visitor 44","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 45","Yes","Yes","Yes"]
[null,"Visitor 45","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 46","Yes","Yes","Yes"]
[null,"Visitor 46","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 47","Yes","Yes","Yes"]
[null,"Visitor 47","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 48","Yes","Yes","Yes"]
[null,"Visitor 48","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 49","Yes","Yes","Yes"]
[null,"Visitor 49","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 50","Yes","Yes","Yes"]
[null,"Visitor 50","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 51","Yes","Yes","Yes"]
[null,"Visitor 51","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 52","Yes","Yes","Yes"]
[null,"Visitor 52","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 53","Yes","Yes","Yes"]
[null,"Visitor 53","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 54","Yes","Yes","Yes"]
[null,"Visitor 54","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 55","Yes","Yes","Yes"]
[null,"Visitor 55","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 56","Yes","Yes","Yes"]
[null,"Visitor 56","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 57","Yes","Yes","Yes"]
[null,"Visitor 57","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 58","Yes","Yes","Yes"]
[null,"Visitor 58","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 59","Yes","Yes","Yes"]
[null,"Visitor 59","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 60","Yes","Yes","Yes"]
[null,"Visitor 60","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 61","Yes","Yes","No"]
[null,"Visitor 61","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 62","Yes","Yes","No"]
[null,"Visitor 62","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 63","Yes","Yes","No"]
[null,"Visitor 63","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 64","Yes","Yes","No"]
[null,"Visitor 64","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 65","Yes","Yes","No"]
[null,"Visitor 65","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 66","Yes","Yes","No"]
[null,"Visitor 66","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 67","Yes","Yes","No"]
[null,"Visitor 67","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 68","Yes","Yes","No"]
[null,"Visitor 68","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 69","Yes","Yes","No"]
[null,"Visitor 69","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 70","Yes","Yes","No"]
[null,"Visitor 70","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 71","Yes","Yes","No"]
[null,"Visitor 71","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 72","Yes","Yes","No"]
[null,"Visitor 72","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 73","Yes","Yes","No"]
[null,"Visitor 73","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 74","Yes","Yes","No"]
[null,"Visitor 74","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 75","Yes","Yes","No"]
[null,"Visitor 75","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 76","Yes","Yes","No"]
[null,"Visitor 76","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 77","Yes","Yes","No"]
[null,"Visitor 77","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 78","Yes","Yes","No"]
[null,"Visitor 78","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 79","Yes","Yes","No"]
[null,"Visitor 79","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 80","Yes","Yes","No"]
[null,"Visitor 80","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 81","Yes","Yes","No"]
[null,"Visitor 81","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 82","Yes","Yes","No"]
[null,"Visitor 82","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 83","Yes","Yes","No"]
[null,"Visitor 83","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 84","Yes","Yes","No"]
[null,"Visitor 84","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 85","Yes","Yes","No"]
[null,"Visitor 85","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 86","Yes","Yes","No"]
[null,"Visitor 86","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 87","Yes","Yes","No"]
[null,"Visitor 87","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 88","Yes","Yes","No"]
[null,"Visitor 88","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 89","Yes","Yes","No"]
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[null,"Visitor 142","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 143","No","No","No"]
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[null,"Visitor 161","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 162","No","No","No"]
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[null,"Visitor 163","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 164","No","No","No"]
[null,"Visitor 164","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 165","No","No","No"]
[null,"Visitor 165","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 166","No","No","No"]
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[null,"Visitor 170","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 171","No","No","No"]
[null,"Visitor 171","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 172","No","No","No"]
[null,"Visitor 172","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 173","No","No","No"]
[null,"Visitor 173","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 174","No","No","No"]
[null,"Visitor 174","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 175","No","No","No"]
[null,"Visitor 175","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 176","No","No","No"]
[null,"Visitor 176","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 177","No","No","No"]
[null,"Visitor 177","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 178","No","No","No"]
[null,"Visitor 178","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 179","No","No","No"]
[null,"Visitor 179","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 180","No","No","No"]
[null,"Visitor 180","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 181","No","No","No"]
[null,"Visitor 181","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 182","No","No","No"]
[null,"Visitor 182","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 183","No","No","No"]
[null,"Visitor 183","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 184","No","No","No"]
[null,"Visitor 184","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 185","No","No","No"]
[null,"Visitor 185","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 186","No","No","No"]
[null,"Visitor 186","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 187","No","No","No"]
[null,"Visitor 187","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 188","No","No","No"]
[null,"Visitor 188","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 189","No","No","No"]
[null,"Visitor 189","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 190","No","No","No"]
[null,"Visitor 190","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 191","No","No","No"]
[null,"Visitor 191","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 192","No","No","No"]
[null,"Visitor 192","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 193","No","No","No"]
[null,"Visitor 193","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 194","No","No","No"]
[null,"Visitor 194","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 195","No","No","No"]
[null,"Visitor 195","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 196","No","No","No"]
[null,"Visitor 196","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 197","No","No","No"]
[null,"Visitor 197","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 198","No","No","No"]
[null,"Visitor 198","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 199","No","No","No"]
[null,"Visitor 199","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 200","No","No","No"]
[null,"Visitor 200","No","Yes"]

{"sheet":"Seattle(1an)","index":22,"n_rows":204,"n_cols":41,"rows_kept":204,"cut":false,"hidden":false,"merged":[]}
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[null,"Travel survey of people who visit Seattle"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor","Visit Space Needle?","Visit Pike's Place Market?","Visit Alki Beach?"]
[null,"Visitor","Visit Space Needle?","Visit Pike's Place Market?",null,"Count of Visitor","Pike's Place Market",null,null,null,null,"P(Space Needle)",{"$f":"I7/I8","v":0.45},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(M4),\"\")","v":"=I7/I8"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"Visitor \"&_xlfn.SEQUENCE(200)","v":"Visitor 1"},{"$f":"IF(_xlfn.SEQUENCE(200)<=45+45,\"Yes\",\"No\")","v":"Yes"},{"$f":"IF(_xlfn.SEQUENCE(200)<=65+65,\"Yes\",\"No\")","v":"Yes"},{"$f":"IF(_xlfn.SEQUENCE(200)<=25+35,\"Yes\",\"No\")","v":"Yes"}]
[null,"Visitor 1","Yes","Yes",null,"Space Needle","No","Yes","Grand Total",null,null,"P(Pike's Place Market)",{"$f":"H8/I8","v":0.65},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(M5),\"\")","v":"=H8/I8"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 2","Yes","Yes","Yes"]
[null,"Visitor 2","No","No",null,"No",58,52,110,null,null,"P(Space Needle AND Pike's Place Market)",{"$f":"H7/I8","v":0.39},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(M6),\"\")","v":"=H7/I8"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 3","Yes","Yes","Yes"]
[null,"Visitor 3","Yes","Yes",null,"Yes",12,78,90,null,null,"P(Space Needle OR Pike's Place Market)",{"$f":"M4+M5-M6","v":0.71000000000000008},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(M7),\"\")","v":"=M4+M5-M6"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 4","Yes","Yes","Yes"]
[null,"Visitor 4","Yes","Yes",null,"Grand Total",70,130,200,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(H8),\"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 5","Yes","Yes","Yes"]
[null,"Visitor 5","Yes","Yes",null,null,null,null,null,null,null,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 6","Yes","Yes","Yes"]
[null,"Visitor 6","Yes","No",null,null,null,null,null,null,null,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 7","Yes","Yes","Yes"]
[null,"Visitor 7","No","Yes",null,null,null,null,null,null,null,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 8","Yes","Yes","Yes"]
[null,"Visitor 8","Yes","Yes",null,null,null,null,null,null,null,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 9","Yes","Yes","Yes"]
[null,"Visitor 9","Yes","Yes",null,null,null,null,null,null,null,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 10","Yes","Yes","Yes"]
[null,"Visitor 10","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 11","Yes","Yes","Yes"]
[null,"Visitor 11","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 12","Yes","Yes","Yes"]
[null,"Visitor 12","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 13","Yes","Yes","Yes"]
[null,"Visitor 13","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 14","Yes","Yes","Yes"]
[null,"Visitor 14","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 15","Yes","Yes","Yes"]
[null,"Visitor 15","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 16","Yes","Yes","Yes"]
[null,"Visitor 16","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 17","Yes","Yes","Yes"]
[null,"Visitor 17","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 18","Yes","Yes","Yes"]
[null,"Visitor 18","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 19","Yes","Yes","Yes"]
[null,"Visitor 19","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 20","Yes","Yes","Yes"]
[null,"Visitor 20","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 21","Yes","Yes","Yes"]
[null,"Visitor 21","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 22","Yes","Yes","Yes"]
[null,"Visitor 22","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 23","Yes","Yes","Yes"]
[null,"Visitor 23","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 24","Yes","Yes","Yes"]
[null,"Visitor 24","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 25","Yes","Yes","Yes"]
[null,"Visitor 25","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 26","Yes","Yes","Yes"]
[null,"Visitor 26","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 27","Yes","Yes","Yes"]
[null,"Visitor 27","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 28","Yes","Yes","Yes"]
[null,"Visitor 28","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 29","Yes","Yes","Yes"]
[null,"Visitor 29","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 30","Yes","Yes","Yes"]
[null,"Visitor 30","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 31","Yes","Yes","Yes"]
[null,"Visitor 31","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 32","Yes","Yes","Yes"]
[null,"Visitor 32","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 33","Yes","Yes","Yes"]
[null,"Visitor 33","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 34","Yes","Yes","Yes"]
[null,"Visitor 34","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 35","Yes","Yes","Yes"]
[null,"Visitor 35","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 36","Yes","Yes","Yes"]
[null,"Visitor 36","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 37","Yes","Yes","Yes"]
[null,"Visitor 37","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 38","Yes","Yes","Yes"]
[null,"Visitor 38","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 39","Yes","Yes","Yes"]
[null,"Visitor 39","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 40","Yes","Yes","Yes"]
[null,"Visitor 40","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 41","Yes","Yes","Yes"]
[null,"Visitor 41","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 42","Yes","Yes","Yes"]
[null,"Visitor 42","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 43","Yes","Yes","Yes"]
[null,"Visitor 43","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 44","Yes","Yes","Yes"]
[null,"Visitor 44","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 45","Yes","Yes","Yes"]
[null,"Visitor 45","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 46","Yes","Yes","Yes"]
[null,"Visitor 46","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 47","Yes","Yes","Yes"]
[null,"Visitor 47","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 48","Yes","Yes","Yes"]
[null,"Visitor 48","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 49","Yes","Yes","Yes"]
[null,"Visitor 49","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 50","Yes","Yes","Yes"]
[null,"Visitor 50","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 51","Yes","Yes","Yes"]
[null,"Visitor 51","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 52","Yes","Yes","Yes"]
[null,"Visitor 52","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 53","Yes","Yes","Yes"]
[null,"Visitor 53","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 54","Yes","Yes","Yes"]
[null,"Visitor 54","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 55","Yes","Yes","Yes"]
[null,"Visitor 55","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 56","Yes","Yes","Yes"]
[null,"Visitor 56","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 57","Yes","Yes","Yes"]
[null,"Visitor 57","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 58","Yes","Yes","Yes"]
[null,"Visitor 58","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 59","Yes","Yes","Yes"]
[null,"Visitor 59","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 60","Yes","Yes","Yes"]
[null,"Visitor 60","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 61","Yes","Yes","No"]
[null,"Visitor 61","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 62","Yes","Yes","No"]
[null,"Visitor 62","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 63","Yes","Yes","No"]
[null,"Visitor 63","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 64","Yes","Yes","No"]
[null,"Visitor 64","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 65","Yes","Yes","No"]
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[null,"Visitor 67","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 68","Yes","Yes","No"]
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[null,"Visitor 69","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 70","Yes","Yes","No"]
[null,"Visitor 70","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 71","Yes","Yes","No"]
[null,"Visitor 71","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 72","Yes","Yes","No"]
[null,"Visitor 72","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 73","Yes","Yes","No"]
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[null,"Visitor 78","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 79","Yes","Yes","No"]
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[null,"Visitor 90","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 91","No","Yes","No"]
[null,"Visitor 91","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 92","No","Yes","No"]
[null,"Visitor 92","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 93","No","Yes","No"]
[null,"Visitor 93","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 94","No","Yes","No"]
[null,"Visitor 94","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 95","No","Yes","No"]
[null,"Visitor 95","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 96","No","Yes","No"]
[null,"Visitor 96","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 97","No","Yes","No"]
[null,"Visitor 97","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 98","No","Yes","No"]
[null,"Visitor 98","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 99","No","Yes","No"]
[null,"Visitor 99","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 100","No","Yes","No"]
[null,"Visitor 100","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 101","No","Yes","No"]
[null,"Visitor 101","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 102","No","Yes","No"]
[null,"Visitor 102","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 103","No","Yes","No"]
[null,"Visitor 103","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 104","No","Yes","No"]
[null,"Visitor 104","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 105","No","Yes","No"]
[null,"Visitor 105","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 106","No","Yes","No"]
[null,"Visitor 106","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 107","No","Yes","No"]
[null,"Visitor 107","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 108","No","Yes","No"]
[null,"Visitor 108","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 109","No","Yes","No"]
[null,"Visitor 109","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 110","No","Yes","No"]
[null,"Visitor 110","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 111","No","Yes","No"]
[null,"Visitor 111","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 112","No","Yes","No"]
[null,"Visitor 112","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 113","No","Yes","No"]
[null,"Visitor 113","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 114","No","Yes","No"]
[null,"Visitor 114","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 115","No","Yes","No"]
[null,"Visitor 115","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 116","No","Yes","No"]
[null,"Visitor 116","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 117","No","Yes","No"]
[null,"Visitor 117","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 118","No","Yes","No"]
[null,"Visitor 118","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 119","No","Yes","No"]
[null,"Visitor 119","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 120","No","Yes","No"]
[null,"Visitor 120","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 121","No","Yes","No"]
[null,"Visitor 121","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 122","No","Yes","No"]
[null,"Visitor 122","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 123","No","Yes","No"]
[null,"Visitor 123","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 124","No","Yes","No"]
[null,"Visitor 124","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 125","No","Yes","No"]
[null,"Visitor 125","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 126","No","Yes","No"]
[null,"Visitor 126","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 127","No","Yes","No"]
[null,"Visitor 127","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 128","No","Yes","No"]
[null,"Visitor 128","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 129","No","Yes","No"]
[null,"Visitor 129","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 130","No","Yes","No"]
[null,"Visitor 130","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 131","No","No","No"]
[null,"Visitor 131","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 132","No","No","No"]
[null,"Visitor 132","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 133","No","No","No"]
[null,"Visitor 133","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 134","No","No","No"]
[null,"Visitor 134","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 135","No","No","No"]
[null,"Visitor 135","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 136","No","No","No"]
[null,"Visitor 136","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 137","No","No","No"]
[null,"Visitor 137","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 138","No","No","No"]
[null,"Visitor 138","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 139","No","No","No"]
[null,"Visitor 139","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 140","No","No","No"]
[null,"Visitor 140","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 141","No","No","No"]
[null,"Visitor 141","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 142","No","No","No"]
[null,"Visitor 142","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 143","No","No","No"]
[null,"Visitor 143","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 144","No","No","No"]
[null,"Visitor 144","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 145","No","No","No"]
[null,"Visitor 145","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 146","No","No","No"]
[null,"Visitor 146","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 147","No","No","No"]
[null,"Visitor 147","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 148","No","No","No"]
[null,"Visitor 148","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 149","No","No","No"]
[null,"Visitor 149","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 150","No","No","No"]
[null,"Visitor 150","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 151","No","No","No"]
[null,"Visitor 151","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 152","No","No","No"]
[null,"Visitor 152","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 153","No","No","No"]
[null,"Visitor 153","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 154","No","No","No"]
[null,"Visitor 154","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 155","No","No","No"]
[null,"Visitor 155","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 156","No","No","No"]
[null,"Visitor 156","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 157","No","No","No"]
[null,"Visitor 157","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 158","No","No","No"]
[null,"Visitor 158","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 159","No","No","No"]
[null,"Visitor 159","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 160","No","No","No"]
[null,"Visitor 160","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 161","No","No","No"]
[null,"Visitor 161","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 162","No","No","No"]
[null,"Visitor 162","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 163","No","No","No"]
[null,"Visitor 163","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 164","No","No","No"]
[null,"Visitor 164","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 165","No","No","No"]
[null,"Visitor 165","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 166","No","No","No"]
[null,"Visitor 166","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 167","No","No","No"]
[null,"Visitor 167","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 168","No","No","No"]
[null,"Visitor 168","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 169","No","No","No"]
[null,"Visitor 169","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 170","No","No","No"]
[null,"Visitor 170","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 171","No","No","No"]
[null,"Visitor 171","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 172","No","No","No"]
[null,"Visitor 172","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 173","No","No","No"]
[null,"Visitor 173","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 174","No","No","No"]
[null,"Visitor 174","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 175","No","No","No"]
[null,"Visitor 175","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 176","No","No","No"]
[null,"Visitor 176","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 177","No","No","No"]
[null,"Visitor 177","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 178","No","No","No"]
[null,"Visitor 178","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 179","No","No","No"]
[null,"Visitor 179","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 180","No","No","No"]
[null,"Visitor 180","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 181","No","No","No"]
[null,"Visitor 181","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 182","No","No","No"]
[null,"Visitor 182","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 183","No","No","No"]
[null,"Visitor 183","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 184","No","No","No"]
[null,"Visitor 184","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 185","No","No","No"]
[null,"Visitor 185","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 186","No","No","No"]
[null,"Visitor 186","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 187","No","No","No"]
[null,"Visitor 187","Yes","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 188","No","No","No"]
[null,"Visitor 188","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 189","No","No","No"]
[null,"Visitor 189","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 190","No","No","No"]
[null,"Visitor 190","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 191","No","No","No"]
[null,"Visitor 191","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 192","No","No","No"]
[null,"Visitor 192","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 193","No","No","No"]
[null,"Visitor 193","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 194","No","No","No"]
[null,"Visitor 194","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 195","No","No","No"]
[null,"Visitor 195","No","No",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 196","No","No","No"]
[null,"Visitor 196","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 197","No","No","No"]
[null,"Visitor 197","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 198","No","No","No"]
[null,"Visitor 198","No","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 199","No","No","No"]
[null,"Visitor 199","Yes","Yes",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 200","No","No","No"]
[null,"Visitor 200","No","Yes"]

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[null,"Survey Question: For Seattle's two tourist sites Space Needle and Pike's Place Market, select one of the following choices:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Seattle Visitor","Space Needle","Pike's Place Market","Where Did They Visit?"]
[null,"Only Space Needle",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 1",1,1,{"$f":"_xlfn.IFS(SUM(AP3:AQ3)=2,$B$5,SUM(AP3:AQ3)=0,$B$6,AND(AP3=1,AQ3=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,"Only Pike's Place Market",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 11",0,1,{"$f":"_xlfn.IFS(SUM(AP4:AQ4)=2,$B$5,SUM(AP4:AQ4)=0,$B$6,AND(AP4=1,AQ4=0),$B$3,TRUE,$B$4)","v":"Only Pike's Place Market"}]
[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 2",0,0,{"$f":"_xlfn.IFS(SUM(AP5:AQ5)=2,$B$5,SUM(AP5:AQ5)=0,$B$6,AND(AP5=1,AQ5=0),$B$3,TRUE,$B$4)","v":"Neither"}]
[null,"Neither",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 3",1,1,{"$f":"_xlfn.IFS(SUM(AP6:AQ6)=2,$B$5,SUM(AP6:AQ6)=0,$B$6,AND(AP6=1,AQ6=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 4",1,1,{"$f":"_xlfn.IFS(SUM(AP7:AQ7)=2,$B$5,SUM(AP7:AQ7)=0,$B$6,AND(AP7=1,AQ7=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,"Results",null,null,null,null,"P(Space Needle)",null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(H8),\"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 5",1,1,{"$f":"_xlfn.IFS(SUM(AP8:AQ8)=2,$B$5,SUM(AP8:AQ8)=0,$B$6,AND(AP8=1,AQ8=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,"Both",null,null,null,null,"P(Pike's Place Market)",null,null,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 6",1,0,{"$f":"_xlfn.IFS(SUM(AP9:AQ9)=2,$B$5,SUM(AP9:AQ9)=0,$B$6,AND(AP9=1,AQ9=0),$B$3,TRUE,$B$4)","v":"Only Space Needle"}]
[null,"Only Pike's Place Market",null,null,null,null,"P(Space Needle AND Pike's Place Market)",null,null,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 7",0,1,{"$f":"_xlfn.IFS(SUM(AP10:AQ10)=2,$B$5,SUM(AP10:AQ10)=0,$B$6,AND(AP10=1,AQ10=0),$B$3,TRUE,$B$4)","v":"Only Pike's Place Market"}]
[null,"Neither",null,null,null,null,"P(Space Needle OR Pike's Place Market)",null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(H11),\"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 8",1,1,{"$f":"_xlfn.IFS(SUM(AP11:AQ11)=2,$B$5,SUM(AP11:AQ11)=0,$B$6,AND(AP11=1,AQ11=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 9",1,1,{"$f":"_xlfn.IFS(SUM(AP12:AQ12)=2,$B$5,SUM(AP12:AQ12)=0,$B$6,AND(AP12=1,AQ12=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 10",0,1,{"$f":"_xlfn.IFS(SUM(AP13:AQ13)=2,$B$5,SUM(AP13:AQ13)=0,$B$6,AND(AP13=1,AQ13=0),$B$3,TRUE,$B$4)","v":"Only Pike's Place Market"}]
[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 12",0,1,{"$f":"_xlfn.IFS(SUM(AP14:AQ14)=2,$B$5,SUM(AP14:AQ14)=0,$B$6,AND(AP14=1,AQ14=0),$B$3,TRUE,$B$4)","v":"Only Pike's Place Market"}]
[null,"Only Space Needle",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 13",1,1,{"$f":"_xlfn.IFS(SUM(AP15:AQ15)=2,$B$5,SUM(AP15:AQ15)=0,$B$6,AND(AP15=1,AQ15=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,"Only Pike's Place Market",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 14",0,1,{"$f":"_xlfn.IFS(SUM(AP16:AQ16)=2,$B$5,SUM(AP16:AQ16)=0,$B$6,AND(AP16=1,AQ16=0),$B$3,TRUE,$B$4)","v":"Only Pike's Place Market"}]
[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 15",1,1,{"$f":"_xlfn.IFS(SUM(AP17:AQ17)=2,$B$5,SUM(AP17:AQ17)=0,$B$6,AND(AP17=1,AQ17=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 16",1,1,{"$f":"_xlfn.IFS(SUM(AP18:AQ18)=2,$B$5,SUM(AP18:AQ18)=0,$B$6,AND(AP18=1,AQ18=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,"Only Pike's Place Market",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 17",1,1,{"$f":"_xlfn.IFS(SUM(AP19:AQ19)=2,$B$5,SUM(AP19:AQ19)=0,$B$6,AND(AP19=1,AQ19=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,"Only Pike's Place Market",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 18",0,0,{"$f":"_xlfn.IFS(SUM(AP20:AQ20)=2,$B$5,SUM(AP20:AQ20)=0,$B$6,AND(AP20=1,AQ20=0),$B$3,TRUE,$B$4)","v":"Neither"}]
[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 19",0,0,{"$f":"_xlfn.IFS(SUM(AP21:AQ21)=2,$B$5,SUM(AP21:AQ21)=0,$B$6,AND(AP21=1,AQ21=0),$B$3,TRUE,$B$4)","v":"Neither"}]
[null,"Only Pike's Place Market",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 20",0,1,{"$f":"_xlfn.IFS(SUM(AP22:AQ22)=2,$B$5,SUM(AP22:AQ22)=0,$B$6,AND(AP22=1,AQ22=0),$B$3,TRUE,$B$4)","v":"Only Pike's Place Market"}]
[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 21",0,0,{"$f":"_xlfn.IFS(SUM(AP23:AQ23)=2,$B$5,SUM(AP23:AQ23)=0,$B$6,AND(AP23=1,AQ23=0),$B$3,TRUE,$B$4)","v":"Neither"}]
[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 22",0,0,{"$f":"_xlfn.IFS(SUM(AP24:AQ24)=2,$B$5,SUM(AP24:AQ24)=0,$B$6,AND(AP24=1,AQ24=0),$B$3,TRUE,$B$4)","v":"Neither"}]
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[null,"Survey Question: For Seattle's two tourist sites Space Needle and Pike's Place Market, select one of the following choices:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Seattle Visitor","Space Needle","Pike's Place Market","Where Did They Visit?"]
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[null,"Results",null,"Visted in Seattle","Frequency",null,"P(Space Needle)",{"$f":"(E12+E9)/E13","v":0.45},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(H8),\"\")","v":"=(E12+E9)/E13"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 5",1,1,{"$f":"_xlfn.IFS(SUM(AP8:AQ8)=2,$B$5,SUM(AP8:AQ8)=0,$B$6,AND(AP8=1,AQ8=0),$B$3,TRUE,$B$4)","v":"Both"}]
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[null,"Both",null,"Grand Total",200,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 10",0,1,{"$f":"_xlfn.IFS(SUM(AP13:AQ13)=2,$B$5,SUM(AP13:AQ13)=0,$B$6,AND(AP13=1,AQ13=0),$B$3,TRUE,$B$4)","v":"Only Pike's Place Market"}]
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[null,"Neither",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 177",0,1,{"$f":"_xlfn.IFS(SUM(AP179:AQ179)=2,$B$5,SUM(AP179:AQ179)=0,$B$6,AND(AP179=1,AQ179=0),$B$3,TRUE,$B$4)","v":"Only Pike's Place Market"}]
[null,"Neither",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 178",0,1,{"$f":"_xlfn.IFS(SUM(AP180:AQ180)=2,$B$5,SUM(AP180:AQ180)=0,$B$6,AND(AP180=1,AQ180=0),$B$3,TRUE,$B$4)","v":"Only Pike's Place Market"}]
[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 179",1,1,{"$f":"_xlfn.IFS(SUM(AP181:AQ181)=2,$B$5,SUM(AP181:AQ181)=0,$B$6,AND(AP181=1,AQ181=0),$B$3,TRUE,$B$4)","v":"Both"}]
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[null,"Only Pike's Place Market",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 184",0,0,{"$f":"_xlfn.IFS(SUM(AP186:AQ186)=2,$B$5,SUM(AP186:AQ186)=0,$B$6,AND(AP186=1,AQ186=0),$B$3,TRUE,$B$4)","v":"Neither"}]
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[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 191",1,1,{"$f":"_xlfn.IFS(SUM(AP193:AQ193)=2,$B$5,SUM(AP193:AQ193)=0,$B$6,AND(AP193=1,AQ193=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,"Neither",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 192",0,1,{"$f":"_xlfn.IFS(SUM(AP194:AQ194)=2,$B$5,SUM(AP194:AQ194)=0,$B$6,AND(AP194=1,AQ194=0),$B$3,TRUE,$B$4)","v":"Only Pike's Place Market"}]
[null,"Only Space Needle",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 193",1,1,{"$f":"_xlfn.IFS(SUM(AP195:AQ195)=2,$B$5,SUM(AP195:AQ195)=0,$B$6,AND(AP195=1,AQ195=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,"Only Pike's Place Market",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 194",1,1,{"$f":"_xlfn.IFS(SUM(AP196:AQ196)=2,$B$5,SUM(AP196:AQ196)=0,$B$6,AND(AP196=1,AQ196=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 195",0,0,{"$f":"_xlfn.IFS(SUM(AP197:AQ197)=2,$B$5,SUM(AP197:AQ197)=0,$B$6,AND(AP197=1,AQ197=0),$B$3,TRUE,$B$4)","v":"Neither"}]
[null,"Neither",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 196",0,1,{"$f":"_xlfn.IFS(SUM(AP198:AQ198)=2,$B$5,SUM(AP198:AQ198)=0,$B$6,AND(AP198=1,AQ198=0),$B$3,TRUE,$B$4)","v":"Only Pike's Place Market"}]
[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 197",1,1,{"$f":"_xlfn.IFS(SUM(AP199:AQ199)=2,$B$5,SUM(AP199:AQ199)=0,$B$6,AND(AP199=1,AQ199=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,"Only Pike's Place Market",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 198",0,1,{"$f":"_xlfn.IFS(SUM(AP200:AQ200)=2,$B$5,SUM(AP200:AQ200)=0,$B$6,AND(AP200=1,AQ200=0),$B$3,TRUE,$B$4)","v":"Only Pike's Place Market"}]
[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 199",1,1,{"$f":"_xlfn.IFS(SUM(AP201:AQ201)=2,$B$5,SUM(AP201:AQ201)=0,$B$6,AND(AP201=1,AQ201=0),$B$3,TRUE,$B$4)","v":"Both"}]
[null,"Both",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Visitor 200",0,1,{"$f":"_xlfn.IFS(SUM(AP202:AQ202)=2,$B$5,SUM(AP202:AQ202)=0,$B$6,AND(AP202=1,AQ202=0),$B$3,TRUE,$B$4)","v":"Only Pike's Place Market"}]
[null,"Neither"]
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[null,"Both"]
[null,"Only Pike's Place Market"]
[null,"Both"]
[null,"Only Pike's Place Market"]

{"sheet":"V(19)","index":25,"n_rows":259,"n_cols":10,"rows_kept":259,"cut":false,"hidden":false,"merged":[[15,1,15,9],[22,1,22,9],[29,1,29,9]]}
[]
[]
[null,"Conditional Probability"]
[null,"The probability of an event given that another related event has already occurred."]
[null,"After the first event has occurred the sample space has changed (gotten smaller)."]
[null,"The two events that make up the Conditional Probability are considered dependent."]
[null,"Notation: P(A | B) = \"Probability of event A, given that event B has already occurred\".   \"|\" = \" given that\"."]
[null,"Examples:"]
[null,"1) This is not conditional probability:"]
[null,"What is probability of pulling one Queen card from a randomly shuffled deck of 52 cards?"]
[null,"There are 4 matching sample points: Q©, Q§, Qª, Q¨"]
[null,"When you calculated the probability, the full Sample Space is intact. Sample Space = 52 cards."]
[null,"P(Pull 1 Queen from deck of cards) = P(Q1) = 4/52"]
[]
[null,"2) This IS conditional probability:"]
[null,"Given that you pulled a Spade Queen card (Qª) as your first card, what is the probability that you can pull a Queen card in the second try?"]
[null,"There are 3 matching sample points: Q©, Q§, Q¨"]
[null,"When you calculated the probability, the Sample Space has changed. Sample Space = 51 cards."]
[null,"P(Pull second Queen given that you already pulled a Queen) = P(Q2 | Q1) = 3/51"]
[null,"The events \"Pulling a Second Queen\" and \"Pulling a First Queen\" are dependent events."]
[]
[null,"3) Calculate the probability that a randomly selected American uses Facebook given that they use YouTube."]
[null,"A random survey of American social media use was conducted and the results are presented in a cross tab report. From the report, calculate the probability that a randomly selected American uses Facebook given that they use YouTube. Said a different way: If a randomly selected American uses YouTube, what is probability that they also use Facebook? "]
[null,null,null,null,null,"Frequency","YouTube"]
[null,null,null,null,null,"Facebook","Not Use YT","Use YT","Total"]
[null,null,null,"Facebook = FB",null,"Not Use FB",16,46,62]
[null,null,null,"YouTube = YT",null,"Use FB",22,116,138]
[null,null,null,null,null,"Total",38,162,200]
[]
[null,"For this problem, the frequencies are given to you, but you can not use the full Sample Space of 200. Because the question askes you to isolate your calculation to just the sample space for YouTube, the Sample Space changes, the denominator that you use is the total number of people who use YouTube, 162."]
[]
[null,"P(Use YT) =",null,null,null,{"$f":"IF(ISBLANK(E32),\"\",\" \"&H28&\"/\"&I28)","v":""},null,"Sample Space not change"]
[null,"P(Use FB AND Use YT) =",null,null,null,{"$f":"IF(ISBLANK(E33),\"\",\" \"&H27&\"/\"&I28)","v":""},null,"Sample Space not change"]
[null,"P(Use FB | Use YT) =",null,null,null,{"$f":"IF(ISBLANK(E34),\"\",\" \"&H27&\"/\"&H28)","v":""},null,"ç Sample Space DOES change"]
[null,"P(Use YT | Use FB) =",null,null,null,{"$f":"IF(ISBLANK(E35),\"\",\" \"&H27&\"/\"&I27)","v":""},null,"ç Sample Space DOES change"]
[]
[null,"Conditional Probability Rule:"]
[null,"P(A | B) = P(A AND B)/P(B) = \"Probability Event A occurs given that Event B has already occurred\"."]
[null,"P(B | A) = P(A AND B)/P(A) =  \"Probability Event B occurs given that Event A has already occurred\"."]
[null,"Textbook notation:"]
[null,"P(A | B) = P(A ∩ B)/P(B) = ",null,null,null,"Joint Probability Table",null,null,null,"AND %"]
[null,"P(B | A) = P(A ∩ B)/P(A) =",null,null,null,"Probability","YouTube"]
[null,null,null,null,null,"Facebook","Not Use YT","Use YT","Total"]
[null,"P(Use FB | Use YT) = ",null,null,null,"Not Use FB",{"$f":"G26:I28/I28","v":0.08},0.23,0.31]
[null,null,null,{"$f":"IF(ISBLANK(D44),\"\",\" \"&H45&\"/\"&H46)","v":""},null,"Use FB",0.11,0.57999999999999996,0.69]
[null,"P(Use YT | Use FB) =",null,null,null,"Total",0.19,0.81,1]
[null,null,null,{"$f":"IF(ISBLANK(D46),\"\",\" \"&H45&\"/\"&I45)","v":""}]
[null,null,null,null,null,null,null,null,null,"Marginal %"]
[]
[]
[]
[]
[null,"P(Not Use YT) = P(B)",null,null,null,0.19]
[null,"P(Use FB AND Not Use YT) = P(A AND B) =",null,null,null,0.11]
[null,"P(A | B) = P(Use FB | Not Use YT) ="]
[]
[]
[]
[null,null,null,null,null,"Probability","Events",null,"Facebook","YouTube"]
[null,"P(Not Use YT) = P(B)",null,null,null,null,"Not Use YT",null,"Use FB","Use YT"]
[null,"P(Use FB AND Not Use YT) = P(A AND B) =",null,null,null,null,"Use FB",null,"Not Use FB","Use YT"]
[null,"P(A | B) = P(Use FB | Not Use YT) =",null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,"Total Records",null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,"P(A | B) = P(Use FB | Not Use YT) =",null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]

{"sheet":"V(19an)","index":26,"n_rows":259,"n_cols":10,"rows_kept":259,"cut":false,"hidden":false,"merged":[[15,1,15,9],[22,1,22,9],[29,1,29,9]]}
[]
[]
[null,"Conditional Probability"]
[null,"The probability of an event given that another related event has already occurred."]
[null,"After the first event has occurred the sample space has changed (gotten smaller)."]
[null,"The two events that make up the Conditional Probability are considered dependent."]
[null,"Notation: P(A | B) = \"Probability of event A, given that event B has already occurred\".   \"|\" = \" given that\"."]
[null,"Examples:"]
[null,"1) This is not conditional probability:"]
[null,"What is probability of pulling one Queen card from a randomly shuffled deck of 52 cards?"]
[null,"There are 4 matching sample points: Q©, Q§, Qª, Q¨"]
[null,"When you calculated the probability, the full Sample Space is intact. Sample Space = 52 cards."]
[null,"P(Pull 1 Queen from deck of cards) = P(Q1) = 4/52"]
[]
[null,"2) This IS conditional probability:"]
[null,"Given that you pulled a Spade Queen card (Qª) as your first card, what is the probability that you can pull a Queen card in the second try?"]
[null,"There are 3 matching sample points: Q©, Q§, Q¨"]
[null,"When you calculated the probability, the Sample Space has changed. Sample Space = 51 cards."]
[null,"P(Pull second Queen given that you already pulled a Queen) = P(Q2 | Q1) = 3/51"]
[null,"The events \"Pulling a Second Queen\" and \"Pulling a First Queen\" are dependent events."]
[]
[null,"3) Calculate the probability that a randomly selected American uses Facebook given that they use YouTube."]
[null,"A random survey of American social media use was conducted and the results are presented in a cross tab report. From the report, calculate the probability that a randomly selected American uses Facebook given that they use YouTube. Said a different way: If a randomly selected American uses YouTube, what is probability that they also use Facebook? "]
[null,null,null,null,null,"Frequency","YouTube"]
[null,null,null,null,null,"Facebook","Not Use YT","Use YT","Total"]
[null,null,null,"Facebook = FB",null,"Not Use FB",16,46,62]
[null,null,null,"YouTube = YT",null,"Use FB",22,116,138]
[null,null,null,null,null,"Total",38,162,200]
[]
[null,"For this problem, the frequencies are given to you, but you can not use the full Sample Space of 200. Because the question askes you to isolate your calculation to just the sample space for YouTube, the Sample Space changes, the denominator that you use is the total number of people who use YouTube, 162."]
[]
[null,"P(Use YT) =",null,null,{"$f":"H28/I28","v":0.81},{"$f":"IF(ISBLANK(E32),\"\",\" \"&H28&\"/\"&I28)","v":" 162/200"},null,"Sample Space not change"]
[null,"P(Use FB AND Use YT) =",null,null,{"$f":"H27/I28","v":0.57999999999999996},{"$f":"IF(ISBLANK(E33),\"\",\" \"&H27&\"/\"&I28)","v":" 116/200"},null,"Sample Space not change"]
[null,"P(Use FB | Use YT) =",null,null,{"$f":"H27/H28","v":0.71604938271604934},{"$f":"IF(ISBLANK(E34),\"\",\" \"&H27&\"/\"&H28)","v":" 116/162"},null,"ç Sample Space DOES change"]
[null,"P(Use YT | Use FB) =",null,null,{"$f":"H27/I27","v":0.84057971014492749},{"$f":"IF(ISBLANK(E35),\"\",\" \"&H27&\"/\"&I27)","v":" 116/138"},null,"ç Sample Space DOES change"]
[]
[null,"Conditional Probability Rule:"]
[null,"P(A | B) = P(A AND B)/P(B) = \"Probability Event A occurs given that Event B has already occurred\"."]
[null,"P(B | A) = P(A AND B)/P(A) =  \"Probability Event B occurs given that Event A has already occurred\"."]
[null,"Textbook notation:"]
[null,"P(A | B) = P(A ∩ B)/P(B) = ",null,null,null,"Joint Probability Table",null,null,null,"AND %"]
[null,"P(B | A) = P(A ∩ B)/P(A) =",null,null,null,"Probability","YouTube"]
[null,null,null,null,null,"Facebook","Not Use YT","Use YT","Total"]
[null,"P(Use FB | Use YT) = ",null,{"$f":"H45/H46","v":0.71604938271604923},null,"Not Use FB",{"$f":"G26:I28/I28","v":0.08},0.23,0.31]
[null,null,null,{"$f":"IF(ISBLANK(D44),\"\",\" \"&H45&\"/\"&H46)","v":" 0.58/0.81"},null,"Use FB",0.11,0.57999999999999996,0.69]
[null,"P(Use YT | Use FB) =",null,{"$f":"H45/I45","v":0.84057971014492749},null,"Total",0.19,0.81,1]
[null,null,null,{"$f":"IF(ISBLANK(D46),\"\",\" \"&H45&\"/\"&I45)","v":" 0.58/0.69"}]
[null,null,null,null,null,null,null,null,null,"Marginal %"]
[]
[]
[]
[]
[null,"P(Not Use YT) = P(B)",null,null,null,0.19]
[null,"P(Use FB AND Not Use YT) = P(A AND B) =",null,null,null,0.11]
[null,"P(A | B) = P(Use FB | Not Use YT) =",null,null,null,{"$f":"F54/F53","v":0.57894736842105265}]
[]
[]
[]
[null,null,null,null,null,"Probability","Events",null,"Facebook","YouTube"]
[null,"P(Not Use YT) = P(B)",null,null,null,{"$f":"COUNTIFS(J60:J259,G60)/F63","v":0.19},"Not Use YT",null,"Use FB","Use YT"]
[null,"P(Use FB AND Not Use YT) = P(A AND B) =",null,null,null,{"$f":"COUNTIFS(I60:I259,G61,J60:J259,G60)/F63","v":0.11},"Use FB",null,"Not Use FB","Use YT"]
[null,"P(A | B) = P(Use FB | Not Use YT) =",null,null,null,{"$f":"F61/F60","v":0.57894736842105265},null,null,"Not Use FB","Not Use YT"]
[null,"Total Records",null,null,null,{"$f":"ROWS(I60:J259)","v":200},null,null,"Use FB","Not Use YT"]
[null,"P(A | B) = P(Use FB | Not Use YT) =",null,null,null,{"$f":"COUNTIFS(I60:I259,G61,J60:J259,G60)/COUNTIFS(J60:J259,G60)","v":0.57894736842105265},null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
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{"sheet":"V(20)","index":27,"n_rows":208,"n_cols":13,"rows_kept":208,"cut":false,"hidden":false,"merged":[[3,1,3,9],[16,1,16,9],[27,1,27,9]]}
[]
[]
[null,"Joint Probability Tables"]
[null,"Joint Probability Tables are cross tabulated tables that that have row and column header conditions and show AND Logical Test Probabilities (Joint Probabilities) on this inside of the table, Single Condition Probabilities (Marginal Probabilities) in the row and column total sections."]
[]
[null,null,"Joint Probability Table",null,null,null,"AND % (Joint Probability)",null,null,null,null,"Survey Data:"]
[null,null,"Probability","YouTube"]
[null,null,"Facebook","Not Use YT","Use YT","Total",null,null,null,null,null,"Facebook","YouTube"]
[null,null,"Not Use FB",0.08,0.23,0.31,null,null,null,null,null,"Use FB","Use YT"]
[null,null,"Use FB",0.11,0.57999999999999996,0.69,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,"Total",0.19,0.81,1,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,"Marginal % (Single Condition Prob.)",null,null,null,null,"Use FB","Use YT"]
[null,"Examples:",null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,"1) Create Joint Probability from a proper data set",null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,"When you have a proper data set with records of data, you can use the PivotTable feature to create a Cross Tabulated Frequency Distribution with the Show Values As % of Grand Total calculation.",null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,"Joint Probability created with PivotTable:",null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,"2) If you are given a cross tabulated report, the fastest way to create a Joint Probability Table is to use a Spilled Array Formula.",null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,"Report given to you:","Frequency","YouTube",null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,"Facebook","Not Use YT","Use YT","Total",null,null,"Not Use FB","Use YT"]
[null,null,null,"Facebook = FB",null,"Not Use FB",16,46,62,null,null,"Use FB","Use YT"]
[null,null,null,"YouTube = YT",null,"Use FB",22,116,138,null,null,"Use FB","Use YT"]
[null,null,null,null,null,"Total",38,162,200,null,null,"Not Use FB","Use YT"]
[null,"Steps to create Joint Probability Table:",null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,"1) Copy first report",null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,"2) Delete numbers",null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,"3) Create spilled array formula",null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,{"$f":"_xlfn.IFNA(\"Joint Probability Table Formula: \"&_xlfn.FORMULATEXT(G37),\"\")","v":""},null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,"PT Prob.",null,null,null,"Use FB","Use YT"]
[null,null,"Single Condition",null,"P(Not Use YT) =",null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,"AND Logical Test",null,"P(Not Use FB AND Use YT) =",null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,"OR Logical Test",null,"P(Not Use FB OR Use YT) =",null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,"Condtional Test",null,"P(Not Use YT | Not Use FB) =",null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,"Old School:",null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
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[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
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[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
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[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]

{"sheet":"V(20an)","index":28,"n_rows":208,"n_cols":18,"rows_kept":208,"cut":false,"hidden":false,"merged":[[3,1,3,9],[16,1,16,9],[27,1,27,9]]}
[]
[]
[null,"Joint Probability Tables"]
[null,"Joint Probability Tables are cross tabulated tables that that have row and column header conditions and show AND Logical Test Probabilities (Joint Probabilities) on this inside of the table, Single Condition Probabilities (Marginal Probabilities) in the row and column total sections."]
[]
[null,null,"Joint Probability Table",null,null,null,"AND % (Joint Probability)",null,null,null,null,"Survey Data:"]
[null,null,"Probability","YouTube"]
[null,null,"Facebook","Not Use YT","Use YT","Total",null,null,null,null,null,"Facebook","YouTube",null,"Count of YouTube","YouTube"]
[null,null,"Not Use FB",0.08,0.23,0.31,null,null,null,null,null,"Use FB","Use YT",null,"Facebook","Not Use YT","Use YT","Grand Total"]
[null,null,"Use FB",0.11,0.57999999999999996,0.69,null,null,null,null,null,"Not Use FB","Use YT",null,"Not Use FB",0.08,0.23,0.31]
[null,null,"Total",0.19,0.81,1,null,null,null,null,null,"Not Use FB","Not Use YT",null,"Use FB",0.11,0.57999999999999996,0.69]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT",null,"Grand Total",0.19,0.81,1]
[null,null,null,null,null,null,"Marginal % (Single Condition Prob.)",null,null,null,null,"Use FB","Use YT"]
[null,"Examples:",null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,"1) Create Joint Probability from a proper data set",null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,"When you have a proper data set with records of data, you can use the PivotTable feature to create a Cross Tabulated Frequency Distribution with the Show Values As % of Grand Total calculation.",null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,"Joint Probability created with PivotTable:",null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,"2) If you are given a cross tabulated report, the fastest way to create a Joint Probability Table is to use a Spilled Array Formula.",null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,"Report given to you:","Frequency","YouTube",null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,"Facebook","Not Use YT","Use YT","Total",null,null,"Not Use FB","Use YT"]
[null,null,null,"Facebook = FB",null,"Not Use FB",16,46,62,null,null,"Use FB","Use YT"]
[null,null,null,"YouTube = YT",null,"Use FB",22,116,138,null,null,"Use FB","Use YT"]
[null,null,null,null,null,"Total",38,162,200,null,null,"Not Use FB","Use YT"]
[null,"Steps to create Joint Probability Table:",null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,"1) Copy first report",null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,"2) Delete numbers",null,null,null,"Joint P. Tbl","YouTube",null,null,null,null,"Use FB","Use YT"]
[null,"3) Create spilled array formula",null,null,null,"Facebook","Not Use YT","Use YT","Total",null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,"Not Use FB",{"$f":"G31:I33/I33","v":0.08},0.23,0.31,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,"Use FB",0.11,0.57999999999999996,0.69,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,"Total",0.19,0.81,1,null,null,"Use FB","Not Use YT"]
[null,null,null,null,{"$f":"_xlfn.IFNA(\"Joint Probability Table Formula: \"&_xlfn.FORMULATEXT(G37),\"\")","v":""},null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,"PT Prob.","Check","Check2",null,"Use FB","Use YT"]
[null,null,"Single Condition",null,"P(Not Use YT) =",null,null,{"$f":"G40","v":0.19},{"$f":"COUNTIFS(M9:M208,G37)/ROWS(L9:M208)","v":0.19},{"$f":"G33/I33","v":0.19},null,"Use FB","Not Use YT"]
[null,null,"AND Logical Test",null,"P(Not Use FB AND Use YT) =",null,null,{"$f":"H38","v":0.23},{"$f":"COUNTIFS(L9:L208,F38,M9:M208,H37)/ROWS(L9:M208)","v":0.23},{"$f":"H31/I33","v":0.23},null,"Use FB","Use YT"]
[null,null,"OR Logical Test",null,"P(Not Use FB OR Use YT) =",null,null,{"$f":"I38+H40-H38","v":0.89000000000000012},{"$f":"ROWS(_xlfn._xlws.FILTER(L9:M208,(L9:L208=F38)+(M9:M208=H37)))/ROWS(L9:M208)","v":0.89},{"$f":"(I31+H33-H31)/I33","v":0.89},null,"Use FB","Use YT"]
[null,null,"Condtional Test",null,"P(Not Use YT | Not Use FB) =",null,null,{"$f":"G38/I38","v":0.25806451612903225},{"$f":"COUNTIFS(M9:M208,G37,L9:L208,F38)/COUNTIFS(L9:L208,F38)","v":0.25806451612903225},{"$f":"G31/I31","v":0.25806451612903225},null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,"Old School:",null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,"Joint P. Tbl","YouTube",null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,"Facebook","Not Use YT","Use YT","Total",null,null,"Use FB","Use YT"]
[null,null,null,null,null,"Not Use FB",{"$f":"G31/$I$33","v":0.08},{"$f":"H31/$I$33","v":0.23},0.31,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,"Use FB",{"$f":"G32/$I$33","v":0.11},{"$f":"H32/$I$33","v":0.57999999999999996},0.69,null,null,"Use FB","Use YT"]
[null,null,null,null,null,"Total",0.19,{"$f":"H33/$I$33","v":0.81},1,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,"Other Alternative based on only dataset:",null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,"Joint P. Tbl","YouTube",null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,"Facebook","Not Use YT","Use YT","Total",null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,"Not Use FB",{"$f":"COUNTIFS(L9:L208,F61:F62,M9:M208,G60:H60)/ROWS(L9:M208)","v":0.08},0.23,{"$f":"COUNTIFS(L9:L208,F61:F62)/ROWS(L9:M208)","v":0.31},null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,"Use FB",0.11,0.57999999999999996,0.69,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,"Total",{"$f":"COUNTIFS(M9:M208,G60:H60)/ROWS(L9:M208)","v":0.19},0.81,{"$f":"SUM(_xlfn.ANCHORARRAY(I61))","v":1},null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Not Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Not Use FB","Use YT"]
[null,null,null,null,null,null,null,null,null,null,null,"Use FB","Use YT"]

{"sheet":"V(21)","index":29,"n_rows":49,"n_cols":14,"rows_kept":49,"cut":false,"hidden":false,"merged":[[42,7,43,8],[48,7,49,8],[14,1,14,9],[20,1,20,9],[28,1,29,3],[28,4,29,6],[28,7,29,9],[32,7,33,8],[38,7,39,8]]}
[]
[]
[null,"Using the Multiplication Law of Probability"]
[null,"Multiplication rule for dependent events:"]
[null,"P(A AND B) = P(B)*P(A | B)"]
[null,"P(A AND B) = P(A)*P(B | A)"]
[null,"Multiplication rule for independent events:"]
[null,"P(A AND B) = P(A)*P(B)"]
[null,"4 examples of calculating the probability for an AND Logical Test:"]
[null,"1) Calculate the probability that both Alphabet stock and Safeway stock will go up next year."]
[null,"2) From a Cross Tabulated Report on American Social Media create a Probability Tree on worksheet."]
[null,"3) From a Cross Tabulated Report on American Social Media create a Probability Tree on paper."]
[null,"4) From a Cross Tabulated Report on Heart Attack & Smoking create a Probability Tree on paper."]
[]
[null,"1) The probability that Alphabet stock (Google) will go up next year is 0.65 and the probability that Safeway stock will go up next year is 0.35. What is probability that both will go up. Assume events are independent."]
[null,null,null,null,null,null,null,null,null,null,null,"P(Q1 AND Q2) = P(Q1)*P(Q2 | Q1)"]
[null,null,null,"P(Alphabet stock will go up in 2023)",null,null,null,0.65,null,null,null,"P(Q1 AND Q2) =",null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(M17),\"\")","v":""}]
[null,null,null,"P(Safeway will go up in 2023)",null,null,null,0.35]
[null,null,null,"P(Both will go up in 2023)",null,null,null,null,{"$f":"IF(ISBLANK(H19),\"\",\" \"&H17&\"*\"&H18)","v":""},null,null,"Probability make sale on a sales call",0.15]
[null,null,null,null,null,null,null,null,null,null,null,"P(Sale on Call 1 AND Sale on Call 2)",null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(M20),\"\")","v":""}]
[null,"2) A random survey of American social media use was conducted. The random experiment will be to first ask: \"Do you use YouTube, Yes, or No?\". The second question will be to ask: \"Do you use Facebook, Yes, or No?\". From a Cross Tab Report shown below, create a Probability Tree that shows Root (Do you use YouTube?), Conditional (Do you use Facebook?) and Joint Probabilities (Do you use both?)."]
[]
[null,null,"Frequency","YouTube"]
[null,null,"Facebook","Not Use YT","Use YT","Total"]
[null,null,"Not Use FB",16,46,62]
[null,null,"Use FB",22,116,138,null,"Multiplication Law of Probability"]
[null,null,"Total",38,162,200,null,"ê","ê","ê"]
[]
[null,"Marginal Probabilities",null,null,"Conditional Probabilities",null,null,"Joint Probabilities (AND)"]
[]
[null,"Use YouTube?",null,null,"Use Facebook?",null,null,"Use Both"]
[]
[null,null,null,null,"Yes =",{"$f":"E26&\"/\"&E27","v":"116/162"},null,{"$f":"$C$929&\"*\"&F33&\" = \"&CHAR(10)&E26&\"/\"&F27","v":"*116/162 = \n116/200"}]
[]
[]
[null,"Yes =",{"$f":"E27&\"/\"&F27","v":"162/200"}]
[]
[]
[null,null,null,null,"No =",{"$f":"E25&\"/\"&E27","v":"46/162"},null,{"$f":"$C$929&\"*\"&F39&\" = \"&CHAR(10)&E25&\"/\"&F27","v":"*46/162 = \n46/200"}]
[]
[]
[]
[null,null,null,null,"Yes =",{"$f":"D26&\"/\"&D27","v":"22/38"},null,{"$f":"$C$939&\"*\"&F43&\" = \"&CHAR(10)&D26&\"/\"&F27","v":"*22/38 = \n22/200"}]
[]
[]
[null,"No =",{"$f":"D27&\"/\"&F27","v":"38/200"}]
[]
[]
[null,null,null,null,"No =",{"$f":"D25&\"/\"&D27","v":"16/38"},null,{"$f":"$C$939&\"*\"&F49&\" = \"&CHAR(10)&D25&\"/\"&F27","v":"*16/38 = \n16/200"}]

{"sheet":"V(21an)","index":30,"n_rows":49,"n_cols":14,"rows_kept":49,"cut":false,"hidden":false,"merged":[[38,7,39,8],[42,7,43,8],[48,7,49,8],[14,1,14,9],[20,1,20,9],[28,1,29,3],[28,4,29,6],[28,7,29,9],[32,7,33,8]]}
[]
[]
[null,"Using the Multiplication Law of Probability"]
[null,"Multiplication rule for dependent events:"]
[null,"P(A AND B) = P(B)*P(A | B)"]
[null,"P(A AND B) = P(A)*P(B | A)"]
[null,"Multiplication rule for independent events:"]
[null,"P(A AND B) = P(A)*P(B)"]
[null,"4 examples of calculating the probability for an AND Logical Test:"]
[null,"1) Calculate the probability that both Alphabet stock and Safeway stock will go up next year."]
[null,"2) From a Cross Tabulated Report on American Social Media create a Probability Tree on worksheet."]
[null,"3) From a Cross Tabulated Report on American Social Media create a Probability Tree on paper."]
[null,"4) From a Cross Tabulated Report on Heart Attack & Smoking create a Probability Tree on paper."]
[]
[null,"1) The probability that Alphabet stock (Google) will go up next year is 0.65 and the probability that Safeway stock will go up next year is 0.35. What is probability that both will go up. Assume events are independent."]
[null,null,null,null,null,null,null,null,null,null,null,"P(Q1 AND Q2) = P(Q1)*P(Q2 | Q1)"]
[null,null,null,"P(Alphabet stock will go up in 2023)",null,null,null,0.65,null,null,null,"P(Q1 AND Q2) =",{"$f":"4/52*3/51","v":4.5248868778280547E-3},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(M17),\"\")","v":"=4/52*3/51"}]
[null,null,null,"P(Safeway will go up in 2023)",null,null,null,0.35]
[null,null,null,"P(Both will go up in 2023)",null,null,null,{"$f":"H17*H18","v":0.22749999999999998},{"$f":"IF(ISBLANK(H19),\"\",\" \"&H17&\"*\"&H18)","v":" 0.65*0.35"},null,null,"Probability make sale on a sales call",0.15]
[null,null,null,null,null,null,null,null,null,null,null,"P(Sale on Call 1 AND Sale on Call 2)",{"$f":"M19*M19","v":2.2499999999999999E-2},{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(M20),\"\")","v":"=M19*M19"}]
[null,"2) A random survey of American social media use was conducted. The random experiment will be to first ask: \"Do you use YouTube, Yes, or No?\". The second question will be to ask: \"Do you use Facebook, Yes, or No?\". From a Cross Tab Report shown below, create a Probability Tree that shows Root (Do you use YouTube?), Conditional (Do you use Facebook?) and Joint Probabilities (Do you use both?)."]
[]
[null,null,"Frequency","YouTube"]
[null,null,"Facebook","Not Use YT","Use YT","Total"]
[null,null,"Not Use FB",16,46,62]
[null,null,"Use FB",22,116,138,null,"Multiplication Law of Probability"]
[null,null,"Total",38,162,200,null,"ê","ê","ê"]
[]
[null,"Marginal Probabilities",null,null,"Conditional Probabilities",null,null,"Joint Probabilities (AND)"]
[]
[null,"Use YouTube?",null,null,"Use Facebook?",null,null,"Use Both"]
[]
[null,null,null,null,"Yes =",{"$f":"E26&\"/\"&E27","v":"116/162"},{"$f":"E26/E27","v":0.71604938271604934},{"$f":"$C$929&\"*\"&F33&\" = \"&CHAR(10)&E26&\"/\"&F27","v":"*116/162 = \n116/200"},null,{"$f":"D36*G33","v":0.57999999999999996}]
[]
[]
[null,"Yes =",{"$f":"E27&\"/\"&F27","v":"162/200"},{"$f":"E27/F27","v":0.81}]
[]
[]
[null,null,null,null,"No =",{"$f":"E25&\"/\"&E27","v":"46/162"},{"$f":"E25/E27","v":0.2839506172839506},{"$f":"$C$929&\"*\"&F39&\" = \"&CHAR(10)&E25&\"/\"&F27","v":"*46/162 = \n46/200"},null,{"$f":"D36*G39","v":0.23}]
[]
[]
[]
[null,null,null,null,"Yes =",{"$f":"D26&\"/\"&D27","v":"22/38"},{"$f":"D26/D27","v":0.57894736842105265},{"$f":"$C$939&\"*\"&F43&\" = \"&CHAR(10)&D26&\"/\"&F27","v":"*22/38 = \n22/200"},null,{"$f":"D46*G43","v":0.11}]
[]
[]
[null,"No =",{"$f":"D27&\"/\"&F27","v":"38/200"},{"$f":"D27/F27","v":0.19}]
[]
[]
[null,null,null,null,"No =",{"$f":"D25&\"/\"&D27","v":"16/38"},{"$f":"D25/D27","v":0.42105263157894735},{"$f":"$C$939&\"*\"&F49&\" = \"&CHAR(10)&D25&\"/\"&F27","v":"*16/38 = \n16/200"},null,{"$f":"D46*G49","v":0.08}]

{"sheet":"NotIndependent","index":31,"n_rows":19,"n_cols":8,"rows_kept":19,"cut":false,"hidden":false,"merged":[]}
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Frequency","YouTube"]
[null,null,null,null,"Facebook","Not Use YT","Use YT","Total"]
[null,null,null,null,"Not Use FB",16,46,62]
[null,null,null,null,"Use FB",22,116,138]
[null,null,null,null,"Total",38,162,200]
[]
[null,null,null,null,{"$f":"\"P(\"&E10&\" | \"&G8&\") = \"&G10&\"/\"&G11&\" = \"&ROUND(G10/G11,4)","v":"P(Use FB | Use YT) = 116/162 = 0.716"}]
[null,null,null,null,{"$f":"\"P(\"&E10&\") = \"&H10&\"/\"&H11&\" = \"&H10/H11","v":"P(Use FB) = 138/200 = 0.69"}]
[]
[null,null,null,null,{"$f":"\"P(\"&E10&\" | \"&G8&\") <> P(\"&E10&\")\"","v":"P(Use FB | Use YT) <> P(Use FB)"}]
[null,null,null,null,{"$f":"ROUND(G10/G11,4)&\" <> \"&H10/H11","v":"0.716 <> 0.69"}]
[]
[null,null,null,null,{"$f":"\"The Events \"&E10&\" and \"&G8&\" are not independent, they are dependent\"","v":"The Events Use FB and Use YT are not independent, they are dependent"}]

{"sheet":"V(22an)","index":32,"n_rows":24,"n_cols":10,"rows_kept":24,"cut":false,"hidden":false,"merged":[[21,6,21,7],[22,6,22,7],[8,1,8,9],[9,1,9,9],[15,3,15,4],[15,6,15,7],[16,3,16,4],[16,6,16,7]]}
[]
[]
[null,"Using Multiplication Law and Bayes' Theorem, Tabular Method can be used:"]
[]
[null,"Example 1:"]
[null,"You're about to take CPA exam, and you heard from last exam that the pass rate was 25%"]
[null,"P(Pass)",null,0.25]
[null,"P(Not Pass)",null,{"$f":"1-D7","v":0.75},{"$f":"IF(ISBLANK(D8),\"\",\" 1 - \"&D7)","v":" 1 - 0.25"}]
[null,"Your plan is to take a preparation course before taking the CPA exam, and therefore you would like to know the probability P(Pass | Took Prep Course)."]
[null,"Then you get new information from a survey that asked people who passed exam, whether or not they took a Preparation Course for the CPA exam:"]
[null,"P(Took Prep Course | Pass)",null,null,0.6]
[null,"P(Took Prep Course | Not Pass)",null,null,0.31]
[]
[null,"For this textbook, these probabilities are given",null,null,null,null,"Use Multiplication Rule to get AND"]
[null,"Prior (Marginal)",null,"Conditional",null,null,"Joint (AND)"]
[null,"P(Pass)",{"$f":"D7","v":0.25},"P(Took Prep Course | Pass)",null,{"$f":"E11","v":0.6},"P(Pass AND Took Prep Course)",null,{"$f":"C16*F16","v":0.15},{"$f":"IF(ISBLANK(I16),\"\",\" \"&C16&\"*\"&F16)","v":" 0.25*0.6"}]
[null,"P(Not Pass)",{"$f":"1-C16","v":0.75},"P(Took Prep Course | Not Pass)",null,0.31,"P(Not Pass AND Took Prep Course)",null,{"$f":"C17*F17","v":0.23249999999999998},{"$f":"IF(ISBLANK(I17),\"\",\" \"&C17&\"*\"&F17)","v":" 0.75*0.31"}]
[null,"Total",{"$f":"SUM(C16:C17)","v":1},null,null,null,null,"Total = Probability Took Prep Course =>",{"$f":"SUM(I16:I17)","v":0.38249999999999995}]
[]
[null,null,null,"Use \"Concept: compare parts to whole\", or Conditional Probability Rule."]
[null,null,null,null,null,null,"Posterior (Revised Probabilities)"]
[null,null,null,null,null,null,"P(Pass |\nTook Prep Course)",null,{"$f":"I16/I18","v":0.39215686274509809},{"$f":"IF(ISBLANK(I22),\"\",\" \"&I16&\"/\"&I17)","v":" 0.15/0.2325"}]
[null,null,null,null,null,null,"P(Pass |\nTook Prep Course)",null,{"$f":"D7*E11/SUMPRODUCT(D7:D8,E11:E12)","v":0.39215686274509809}]
[null,null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(I23),\"\")","v":"=D7*E11/SUMPRODUCT(D7:D8,E11:E12)"}]

{"sheet":"BT-CPA","index":33,"n_rows":10006,"n_cols":11,"rows_kept":10006,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Survey of people who took CPA exam:"]
[null,"Q1: What was your score (0-1000)?"]
[null,"Q2: Did you take a Preparation Course (PC or NPC)?"]
[]
[null,"Score","Prep Course",null,"P(Not Pass | Took PC) ="]
[null,927,"Not Take Prep Course",null,"P(Pass | Took PC) =",null,null,null,null,null,"P(Pass | Took PC) = P(Pass AND Took PC)/P(Took PC)"]
[null,343,"Not Take Prep Course"]
[null,757,"Took Prep Course",null,"P(Not Pass | Took PC) =",null,null,null,null,null,"# Took Prep Course"]
[null,834,"Took Prep Course",null,"P(Pass | Took PC) =",null,null,null,null,null,"# Pass AND Took PC"]
[null,641,"Not Take Prep Course",null,null,null,null,null,null,null,"P(Pass | Took PC) ="]
[null,204,"Not Take Prep Course"]
[null,139,"Not Take Prep Course",null,null,null,null,null,null,null,"Criteria 1"]
[null,475,"Not Take Prep Course",null,null,null,null,null,null,null,"Criteria 2"]
[null,197,"Took Prep Course"]
[null,757,"Took Prep Course"]
[null,143,"Not Take Prep Course"]
[null,46,"Not Take Prep Course"]
[null,108,"Not Take Prep Course"]
[null,544,"Took Prep Course"]
[null,535,"Not Take Prep Course"]
[null,363,"Not Take Prep Course"]
[null,891,"Took Prep Course"]
[null,891,"Took Prep Course"]
[null,145,"Not Take Prep Course"]
[null,688,"Not Take Prep Course"]
[null,420,"Not Take Prep Course"]
[null,817,"Not Take Prep Course"]
[null,768,"Took Prep Course"]
[null,885,"Took Prep Course"]
[null,676,"Not Take Prep Course"]
[null,536,"Took Prep Course"]
[null,744,"Not Take Prep Course"]
[null,917,"Took Prep Course"]
[null,623,"Not Take Prep Course"]
[null,989,"Not Take Prep Course"]
[null,649,"Not Take Prep Course"]
[null,251,"Took Prep Course"]
[null,383,"Not Take Prep Course"]
[null,822,"Not Take Prep Course"]
[null,643,"Took Prep Course"]
[null,877,"Took Prep Course"]
[null,46,"Not Take Prep Course"]
[null,706,"Not Take Prep Course"]
[null,816,"Not Take Prep Course"]
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{"sheet":"BT-CPA (an)","index":34,"n_rows":10006,"n_cols":13,"rows_kept":10006,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Survey of people who took CPA exam:"]
[null,"Q1: What was your score (0-1000)?"]
[null,"Q2: Did you take a Preparation Course (PC or NPC)?"]
[]
[null,"Score","Prep Course",null,"P(Not Pass | Took PC) =",null,{"$f":"G15/G17","v":0.60784313725490191},null,{"$f":"IF(ISBLANK(G6),\"\",\" \"&G13&\"/\"&ROUND($G$15,4))","v":" /2325"}]
[null,927,"Not Take Prep Course",null,"P(Pass | Took PC) =",null,{"$f":"G16/G17","v":0.39215686274509803},null,{"$f":"IF(ISBLANK(G7),\"\",\" \"&G14&\"/\"&ROUND($G$15,4))","v":" Took PC/2325"},null,"P(Pass | Took PC) = P(Pass AND Took PC)/P(Took PC)"]
[null,343,"Not Take Prep Course"]
[null,757,"Took Prep Course",null,"P(Not Pass | Took PC) =",null,{"$f":"G21:G22/G23","v":0.60784313725490202},null,null,null,"# Took Prep Course",null,{"$f":"COUNTIFS(C7:C10006,L14)","v":3825}]
[null,834,"Took Prep Course",null,"P(Pass | Took PC) =",null,0.39215686274509803,null,null,null,"# Pass AND Took PC",null,{"$f":"COUNTIFS(C7:C10006,L14,B7:B10006,\">=\"&L13)","v":1500}]
[null,641,"Not Take Prep Course",null,null,null,null,null,null,null,"P(Pass | Took PC) =",null,{"$f":"M10/M9","v":0.39215686274509803}]
[null,204,"Not Take Prep Course"]
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[null,475,"Not Take Prep Course",null,"Score","Not Take PC","Took PC","Grand Total",null,null,"Criteria 2","Took Prep Course"]
[null,197,"Took Prep Course",null,"Not Pass",5175,2325,7500]
[null,757,"Took Prep Course",null,"Pass",1000,1500,2500]
[null,143,"Not Take Prep Course",null,"Grand Total",6175,3825,10000]
[null,46,"Not Take Prep Course"]
[null,108,"Not Take Prep Course",null,"Joint Pr. T.","Prep Course"]
[null,544,"Took Prep Course",null,"Score","Not Take PC","Took PC","Grand Total"]
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[null,363,"Not Take Prep Course",null,"Pass",0.1,0.15,0.25]
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[null,420,"Not Take Prep Course",null,"P(Pass)",0.25,"P(PC | Pass)",0.6,"P(Pass AND PC)",null,{"$f":"F27*H27","v":0.15},"P(Pass | PC)",{"$f":"K27:K28/K29","v":0.39215686274509809}]
[null,817,"Not Take Prep Course",null,"P(Not Pass)",{"$f":"1-F27","v":0.75},"P(PC | Not Pass)",0.31,"P(NOT Pass AND PC)",null,{"$f":"F28*H28","v":0.23249999999999998},"P(NOT Pass | PC)",0.60784313725490202]
[null,768,"Took Prep Course",null,null,null,null,null,null,"P(PC)",{"$f":"SUM(K27:K28)","v":0.38249999999999995}]
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{"sheet":"Garage-BT","index":35,"n_rows":15,"n_cols":10,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
["Array: Bayes' Theorem"]
["SUMPRODUCT function"]
[]
[null,"Events:"]
["Prior","GO = Garage Open"]
["Prior","GNO = Garage Not Open"]
[null,"SS = Stuff Stolen"]
[null,"SNS = Stuff Not Stolen"]
[]
["Event & P(x)","Prior Probability or Marginal Prob","P(x)","Conditional Probability","P(x)","Joint Probability","P(x)","Posterior Probability"]
["Leave garage open = P(GO)",0.2,"Stuff Stolen, Given Leave Garage Open = P(SS | GO)",0.05,"P(GO AND SS)",null,"P(GO | SS)",null,null,"Conditional = P(A AND B)/P(B)"]
["Not Leave garage open = P(GNO)",null,"Stuff Stolen, Given Not Leave Garage Open = P(SS | GNO)",0.01,"P(GNO AND SS)",null,"P(GNO | SS)",null,null,"Conditional = P(A AND B)/P(B)"]
[null,null,null,null,"P(Stuff Stolen)"]
[]
["Single Cell Formula:","P(GO | SS)",null,null,"P(SNS)"]

{"sheet":"Garage-BT (an)","index":36,"n_rows":15,"n_cols":10,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
["Array: Bayes' Theorem"]
["SUMPRODUCT function"]
[]
[null,"Events:"]
["Prior","GO = Garage Open"]
["Prior","GNO = Garage Not Open"]
[null,"SS = Stuff Stolen"]
[null,"SNS = Stuff Not Stolen"]
[]
["Event & P(x)","Prior Probability or Marginal Prob","P(x)","Conditional Probability","P(x)","Joint Probability","P(x)","Posterior Probability"]
["Leave garage open = P(GO)",0.2,"Stuff Stolen, Given Leave garage open = P(SS | GO)",0.05,"P(GO AND SS)",{"$f":"B11:B12*D11:D12","v":1.0000000000000002E-2},"P(GO | SS)",{"$f":"_xlfn.ANCHORARRAY(F11)/F13","v":0.55555555555555558},null,"Conditional = P(A AND B)/P(B)"]
["Not Leave garage open = P(GNO)",{"$f":"1-B11","v":0.8},"Stuff Stolen, Given Not Leave garage open = P(SS | GNO)",0.01,"P(GNO AND SS)",8.0000000000000002E-3,"P(GNO | SS)",0.44444444444444442,null,"Conditional = P(A AND B)/P(B)"]
[null,{"$f":"SUM(B11:B12)","v":1},null,null,"P(Stuff Stolen)",{"$f":"SUM(_xlfn.ANCHORARRAY(F11))","v":1.8000000000000002E-2}]
[]
["Single Cell Formula:","P(GO | SS)",{"$f":"(B11*D11)/SUMPRODUCT(B11:B12,D11:D12)","v":0.55555555555555558},null,"P(SNS)",{"$f":"1-F13","v":0.98199999999999998}]