{"text_format":"1","workbook":"xlsx","n_sheets":35,"sheets":["(1)","(2)","(3)","(4)","(5)","(6)","(7)","(8)","(9)","(11x)","(11)","(12)","(14)","(15)","(16)","(18)","(19)","(21)","(22)","(23)","(25)","(27old)","(28)","(29)","(30)","(31)","(32-old)","(32)","(36)","(37-old)","(37)","(39)","(44)","(52-53)","58"],"not_rendered":{"charts":0,"images":0,"macros":0,"external_links":0,"defined_names":2,"comments":4,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"(1)","index":0,"n_rows":4,"n_cols":4,"rows_kept":4,"cut":false,"hidden":false,"merged":[]}
["Step","Outcomes",null,"Total Experimental Outcomes (Sample Points) for Entire Experiment?"]
["Step1",3,null,{"$f":"B2&\"*\"&B3&\"*\"&B4","v":"3*2*4"}]
["Step2",2,null,{"$f":"B2*B3*B4","v":24}]
["Step3",4]

{"sheet":"(2)","index":1,"n_rows":48,"n_cols":7,"rows_kept":48,"cut":false,"hidden":false,"merged":[]}
["Find the number of combinations and list them"]
[]
["Items",null,"N",{"$f":"COUNTA(A4:A9)","v":6},"all the items"]
["A",null,"n",3,"subset of items or items selected"]
["B",null,"Combinations",{"$f":"FACT(D3)/(FACT(D4)*FACT(D3-D4))","v":20}]
["C",null,"COMBIN",{"$f":"COMBIN(D3,D4)","v":20}]
["D"]
["E",null,"# of unique Experimental Outcomes (w/ N = 6, n = 3)\nor\nTotal Number of Experimental Outcomes (w/ N = 6, n = 3)\nor\n# of combinations of N objects taken n at a time","Item 1","Item 2","Item 3","Sample Point\nor\nExperimental Outcome"]
["F",null,1,"A","B","C",{"$f":"\"(\"&D9&\",\"&E9&\",\"&F9&\")\"","v":"(A,B,C)"}]
[null,null,2,"A","B","D",{"$f":"\"(\"&D10&\",\"&E10&\",\"&F10&\")\"","v":"(A,B,D)"}]
[null,null,3,"A","B","E","(A,B,E)"]
[null,null,4,"A","B","F","(A,B,F)"]
[null,null,5,"A","C","D","(A,C,D)"]
[null,null,6,"A","C","E","(A,C,E)"]
[null,null,7,"A","C","F","(A,C,F)"]
[null,null,8,"A","D","E","(A,D,E)"]
[null,null,9,"A","D","F","(A,D,F)"]
[null,null,10,"A","E","F","(A,E,F)"]
[null,null,11,"B","C","D","(B,C,D)"]
[null,null,12,"B","C","E","(B,C,E)"]
[null,null,13,"B","C","F","(B,C,F)"]
[null,null,14,"B","D","E","(B,D,E)"]
[null,null,15,"B","D","F","(B,D,F)"]
[null,null,16,"B","E","F","(B,E,F)"]
[null,null,17,"C","D","E","(C,D,E)"]
[null,null,18,"C","D","F","(C,D,F)"]
[null,null,19,"C","E","F","(C,E,F)"]
[null,null,20,"D","E","F","(D,E,F)"]
[]
[null,null,"S = {(A,B,C), (A,B,D), (A,B,E), (A,B,F), (A,C,D), (A,C,E), (A,C,F), (A,D,E), (A,D,F), (A,E,F), (B,C,D), (B,C,E), (B,C,F), (B,D,E), (B,D,F), (B,E,F), (C,D,E), (C,D,F), (C,E,F), (D,E,F)}"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,"Formula to create S ==> =\"S = {\"&MCONCAT(G9:G28,\", \")&\"}\", entered with Ctrl = Shift = Enter"]

{"sheet":"(3)","index":2,"n_rows":14,"n_cols":5,"rows_kept":14,"cut":false,"hidden":false,"merged":[]}
["Find the number of permutations and list them"]
[]
["Items",null,"N",{"$f":"COUNTA(A4:A9)","v":6},"all the items"]
["A",null,"n",3,"subset of items or items selected"]
["B",null,"permutations",{"$f":"FACT(D3)/FACT(D3-D4)","v":120}]
["C",null,"PERMUT",{"$f":"PERMUT(D3,D4)","v":120}]
["D"]
["E",null,"All permutations of B, D, F"]
["F",null,"BDF"]
[null,null,"BFD"]
[null,null,"DBF"]
[null,null,"DFB"]
[null,null,"FBD"]
[null,null,"FDB"]

{"sheet":"(4)","index":3,"n_rows":35,"n_cols":17,"rows_kept":35,"cut":false,"hidden":false,"merged":[]}
["Experiment of tossing coin three times"]
["Steps in Experiment",3]
["Outcomes Step 1",2]
["Outcomes Step 2",2]
["Outcomes Step 3",2,null,null,null,"Success ="]
["Total Experimental Outcomes (Sample Points)",{"$f":"PRODUCT(B3:B5)","v":8},null,null,null,"Heads"]
["P(for each) =",{"$f":"1/B6","v":0.125},null,null,null,{"$f":"\"Notation for \"&F6&\" is \"&LEFT(F6,1)","v":"Notation for Heads is H"}]
[null,null,null,null,null,{"$f":"LEFT(F6,1)","v":"H"}]
["Number of Sample Points (# of Unique Experimental Outcomes)","Toss 1","Toss 2","Toss 3","Sample Point\nor Experimental Outcome","Probability of Sample Point (classical = each is equally likely)",null,"Number of Heads",null,"Event = Number of Heads (Category)","Frequency","Formula","Relative Frequency","Probability by Adding","Formula","Probability Multiplying (each equally likely)","Formula"]
[1,"H","H","H",{"$f":"\"(\"&B10&\", \"&C10&\", \"&D10&\")\"","v":"(H, H, H)"},{"$f":"COUNTIF($E$10:$E$17,E10)/$B$6","v":0.125},null,{"$f":"COUNTIF(B10:D10,$F$8)","v":3},null,3,{"$f":"COUNTIF($H$10:$H$17,J10)","v":1},{"$f":"\" \"&K10&\"/\"&$K$14&\" =\"","v":" 1/8 ="},{"$f":"K10/$K$14","v":0.125},{"$f":"SUMIF($H$10:$H$17,J10,$F$10:$F$17)","v":0.125}," =SUMIF($I$10:$I$17,L10,$F$10:$F$17)",{"$f":"1/$B$6*K10","v":0.125}," =1/$B$6*M10"]
[2,"T","H","H","(T, H, H)",0.125,null,2,null,2,{"$f":"COUNTIF($H$10:$H$17,J11)","v":3},{"$f":"\" \"&K11&\"/\"&$K$14&\" =\"","v":" 3/8 ="},{"$f":"K11/$K$14","v":0.375},{"$f":"SUMIF($H$10:$H$17,J11,$F$10:$F$17)","v":0.375}," =SUMIF($I$10:$I$17,L11,$F$10:$F$17)",{"$f":"1/$B$6*K11","v":0.375}," =1/$B$6*M11"]
[3,"H","T","H","(H, T, H)",0.125,null,2,null,1,{"$f":"COUNTIF($H$10:$H$17,J12)","v":3},{"$f":"\" \"&K12&\"/\"&$K$14&\" =\"","v":" 3/8 ="},{"$f":"K12/$K$14","v":0.375},{"$f":"SUMIF($H$10:$H$17,J12,$F$10:$F$17)","v":0.375}," =SUMIF($I$10:$I$17,L12,$F$10:$F$17)",{"$f":"1/$B$6*K12","v":0.375}," =1/$B$6*M12"]
[4,"H","H","T","(H, H, T)",0.125,null,2,null,0,{"$f":"COUNTIF($H$10:$H$17,J13)","v":1},{"$f":"\" \"&K13&\"/\"&$K$14&\" =\"","v":" 1/8 ="},{"$f":"K13/$K$14","v":0.125},{"$f":"SUMIF($H$10:$H$17,J13,$F$10:$F$17)","v":0.125}," =SUMIF($I$10:$I$17,L13,$F$10:$F$17)",{"$f":"1/$B$6*K13","v":0.125}," =1/$B$6*M13"]
[5,"T","T","H","(T, T, H)",0.125,null,1,null,null,{"$f":"SUM(K10:K13)","v":8}]
[6,"T","H","T","(T, H, T)",0.125,null,1]
[7,"H","T","T","(H, T, T)",0.125,null,1]
[8,"T","T","T","(T, T, T)",0.125,null,0]
[]
[null,"Step 1","Step 2","Step 3","List of Sample Points (Experimental Outcomes)"]
[]
[null,null,null,"Head","(H, H, H)"]
[null,null,"Head"]
[null,null,null,"Tail","(H, H, T)"]
[null,"Head"]
[null,null,null,"Head","(H, T, H)"]
[null,null,"Tail"]
[null,null,null,"Tail","(H, T, T)"]
[]
[null,null,null,"Head","(T, H, H)"]
[null,null,"Head"]
[null,null,null,"Tail","(T, H, T)"]
[null,"Tail"]
[null,null,null,"Head","(T, T, H)"]
[null,null,"Tail"]
[null,null,null,"Tail","(T, T, T)"]

{"sheet":"(5)","index":4,"n_rows":9,"n_cols":4,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
[null,null,null,"Requirement 1\n0 <= P(Ei) >= 1"]
["Experimental Outcome 1","E1",{"$f":"1/COUNTA($A$2:$A$6)","v":0.2},{"$f":"AND(C2>=0,C2<=1)","v":true}]
["Experimental Outcome 2","E2",{"$f":"1/COUNTA($A$2:$A$6)","v":0.2},{"$f":"AND(C3>=0,C3<=1)","v":true}]
["Experimental Outcome 3","E3",{"$f":"1/COUNTA($A$2:$A$6)","v":0.2},{"$f":"AND(C4>=0,C4<=1)","v":true}]
["Experimental Outcome 4","E4",{"$f":"1/COUNTA($A$2:$A$6)","v":0.2},{"$f":"AND(C5>=0,C5<=1)","v":true}]
["Experimental Outcome 5","E5",{"$f":"1/COUNTA($A$2:$A$6)","v":0.2},{"$f":"AND(C6>=0,C6<=1)","v":true}]
[null,"Requirement 2 \nΣP(Ei) = 1",{"$f":"SUM(C2:C6)","v":1}]
[]
["Method used = Classical, because all experimental outcomes were equally likely."]

{"sheet":"(6)","index":5,"n_rows":10,"n_cols":6,"rows_kept":10,"cut":false,"hidden":false,"merged":[]}
["Outcomes",3]
["Experiment Repeated",50]
[]
[null,null,{"$f":"\"Number of times that Experimental Outcome Occurred in \"&B2&\" tries\"","v":"Number of times that Experimental Outcome Occurred in 50 tries"},null,"Relative Frequency","Requirement 1\n0 <= P(Ei) >= 1"]
["Experimental Outcome 1","E1",20,null,{"$f":"C5/$C$8","v":0.4},{"$f":"AND(E5>=0,E5<=1)","v":true}]
["Experimental Outcome 2","E2",13,null,{"$f":"C6/$C$8","v":0.26},{"$f":"AND(E6>=0,E6<=1)","v":true}]
["Experimental Outcome 3","E3",17,null,{"$f":"C7/$C$8","v":0.34},{"$f":"AND(E7>=0,E7<=1)","v":true}]
[null,null,{"$f":"SUM(C5:C7)","v":50},"Requirement 2 \nΣP(Ei) = 1",{"$f":"SUM(E5:E7)","v":1}]
[]
[null,null,"Method used = Relative Frequency"]

{"sheet":"(7)","index":6,"n_rows":7,"n_cols":3,"rows_kept":7,"cut":false,"hidden":false,"merged":[]}
["E1",{"$f":"\"P(\"&A1&\")\"","v":"P(E1)"},0.1]
["E2",{"$f":"\"P(\"&A2&\")\"","v":"P(E2)"},0.15]
["E3",{"$f":"\"P(\"&A3&\")\"","v":"P(E3)"},0.4]
["E4",{"$f":"\"P(\"&A4&\")\"","v":"P(E4)"},0.2]
[null,null,{"$f":"SUM(C1:C4)","v":0.85000000000000009}]
[null,null,"Not valid because they violate:"]
[null,null,"Requirement 2 \nΣP(Ei) = 1"]

{"sheet":"(8)","index":7,"n_rows":21,"n_cols":7,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["Steps","Steps","Outcome 1","Notation 1","Outcome 2","Notation 2","Number of Outcomes For Step"]
["Step 1","Review by planning commission","Positive Recommendation","PR","Negative Recommendation","NR",{"$f":"COUNTA(C2,E2)","v":2}]
["Step 2","Final Decision by City Council","Approve","A","Disapprove","D",{"$f":"COUNTA(C3,E3)","v":2}]
[]
["Experiment","Developer submits application for zoning change"]
["# of Steps For Zoning Changes =",2]
["Total Sample Points (Experimental Outcomes)",{"$f":"G2*G3","v":4}]
[]
[null,"Step 1","Step 2","List of All Sample Points (Experimental Outcomes)"]
[]
[]
[null,null,{"$f":"$D$3","v":"A"},{"$f":"\"(\"&$B$13&\", \"&C12&\")\"","v":"(PR, A)"},{"$f":"C2&\", \"&C3","v":"Positive Recommendation, Approve"}]
[null,{"$f":"D2","v":"PR"}]
[null,null,{"$f":"$F$3","v":"D"},{"$f":"\"(\"&$B$13&\", \"&C14&\")\"","v":"(PR, D)"},{"$f":"C2&\", \"&E3","v":"Positive Recommendation, Disapprove"}]
[]
[null,null,{"$f":"$D$3","v":"A"},{"$f":"\"(\"&$B$17&\", \"&C16&\")\"","v":"(NR, A)"},{"$f":"E2&\", \"&C3","v":"Negative Recommendation, Approve"}]
[null,{"$f":"F2","v":"NR"}]
[null,null,{"$f":"$F$3","v":"D"},{"$f":"\"(\"&$B$17&\", \"&C18&\")\"","v":"(NR, D)"},{"$f":"E2&\", \"&E3","v":"Negative Recommendation, Disapprove"}]
[]
[{"$f":"\"List of sample Points S = {\"&D12&\", \"&D14&\", \"&D16&\", \"&D18&\"}\"","v":"List of sample Points S = {(PR, A), (PR, D), (NR, A), (NR, D)}"}]
[{"$f":"\"List of sample Points S = {\"&E12&\", \"&E14&\", \"&E16&\", \"&E18&\"}\"","v":"List of sample Points S = {Positive Recommendation, Approve, Positive Recommendation, Disapprove, Negative Recommendation, Approve, Negative Recommendation, Disapprove}"}]

{"sheet":"(9)","index":8,"n_rows":7,"n_cols":2,"rows_kept":7,"cut":false,"hidden":false,"merged":[]}
["Simple Random sampling uses a sample size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population"]
[]
["Random Sample means we randomly select a subset of accounts from the population"]
["Population of bank accounts = ",50]
["Sample size =",4]
["Total Number of Samples possible =",{"$f":"FACT(B4)/(FACT(B5)*FACT(B4-B5))","v":230300}]
["Total Number of Samples possible =",{"$f":"COMBIN(B4,B5)","v":230300}]

{"sheet":"(11x)","index":9,"n_rows":34,"n_cols":14,"rows_kept":34,"cut":false,"hidden":true,"merged":[]}
[null,null,"Driver Using Seat Belt",null,null,"c",null,null,"d"]
[null,"Region","Yes","No","Total","Proportion of Yes within Region","Proportion of No within Region","Requirement 2"]
[null,"NE",148,52,{"$f":"SUM(C3:D3)","v":200},{"$f":"C3/$E3","v":0.74},{"$f":"D3/$E3","v":0.26},{"$f":"SUM(F3:G3)","v":1}]
[null,"MW",162,54,{"$f":"SUM(C4:D4)","v":216},{"$f":"C4/$E4","v":0.75},0.25,{"$f":"SUM(F4:G4)","v":1}]
[null,"S",296,74,{"$f":"SUM(C5:D5)","v":370},0.8,0.2,{"$f":"SUM(F5:G5)","v":1}]
[null,"W",252,48,{"$f":"SUM(C6:D6)","v":300},0.84,0.16,{"$f":"SUM(F6:G6)","v":1}]
[null,"Total",{"$f":"SUM(C3:C6)","v":858},{"$f":"SUM(D3:D6)","v":228},{"$f":"SUM(C7:D7)","v":1086}]
[]
["a",{"$f":"\"P(\"&$C$1&\" = \"&C2&\") = \"&C7&\"/\"&E7","v":"P(Driver Using Seat Belt = Yes) = 858/1086"},{"$f":"C7/E7","v":0.79005524861878451}]
["b",{"$f":"\"Yes because \"&TEXT(C9,\"0.00%\")&\" > .78\"","v":"Yes because 79.01% > .78"}]
["c",{"$f":"\"West has highest at \"&F6","v":"West has highest at 0.84"}]
[]
["d",{"$f":"B2","v":"Region"},"Proportion of drivers  in sample from each region of country"]
[null,"NE",{"$f":"E3/$E$7","v":0.18416206261510129}]
[null,"MW",{"$f":"E4/$E$7","v":0.19889502762430938}]
[null,"S",{"$f":"E5/$E$7","v":0.3406998158379374}]
[null,"W",{"$f":"E6/$E$7","v":0.27624309392265195}]
[null,"Total",{"$f":"SUM(C14:C17)","v":1}]
[]
[null,"The South had the most drivers selected"]
[null,"The West had the second most"]
[]
["e","Yes, .34 for South + .286 for West = .626 shows that 62.6% of the survey came from the two highest usage regions. The .79 probability may be high."]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,"Proportions of usage of regions compared to whole country"]
[null,null,null,null,null,null,null,null,null,null,{"$f":"\"P(\"&$B3&\" = \"&C$2&\") =\"","v":"P(NE = Yes) ="},{"$f":"C3/$E$7","v":0.13627992633517497},{"$f":"\"P(\"&$B3&\" = \"&D$2&\") =\"","v":"P(NE = No) ="},{"$f":"D3/$E$7","v":4.7882136279926338E-2}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"\"P(\"&$B4&\" = \"&C$2&\") =\"","v":"P(MW = Yes) ="},{"$f":"C4/$E$7","v":0.14917127071823205},{"$f":"\"P(\"&$B4&\" = \"&D$2&\") =\"","v":"P(MW = No) ="},{"$f":"D4/$E$7","v":4.9723756906077346E-2}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"\"P(\"&$B5&\" = \"&C$2&\") =\"","v":"P(S = Yes) ="},{"$f":"C5/$E$7","v":0.27255985267034993},{"$f":"\"P(\"&$B5&\" = \"&D$2&\") =\"","v":"P(S = No) ="},{"$f":"D5/$E$7","v":6.8139963167587483E-2}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"\"P(\"&$B6&\" = \"&C$2&\") =\"","v":"P(W = Yes) ="},{"$f":"C6/$E$7","v":0.23204419889502761},{"$f":"\"P(\"&$B6&\" = \"&D$2&\") =\"","v":"P(W = No) ="},{"$f":"D6/$E$7","v":4.4198895027624308E-2}]
[]
[null,null,null,null,null,null,null,null,null,null,"Sum of all must = 1",{"$f":"SUM(L29:L32,N29:N32)","v":1}]

{"sheet":"(11)","index":10,"n_rows":11,"n_cols":9,"rows_kept":11,"cut":false,"hidden":false,"merged":[]}
["Region","DOT-compliant","Noncompliant","Total",null,"DOT compliant by Region","P(compliant)","P(Not compliant)","Total"]
["NE",96,62,{"$f":"SUM(B2:C2)","v":158},null,{"$f":"\"P(\"&A2&\")\"","v":"P(NE)"},{"$f":"B2/$D2","v":0.60759493670886078},{"$f":"C2/$D2","v":0.39240506329113922},{"$f":"SUM(G2:H2)","v":1}]
["MW",86,43,{"$f":"SUM(B3:C3)","v":129},null,{"$f":"\"P(\"&A3&\")\"","v":"P(MW)"},{"$f":"B3/$D3","v":0.66666666666666663},{"$f":"C3/$D3","v":0.33333333333333331},1]
["S",92,49,{"$f":"SUM(B4:C4)","v":141},null,{"$f":"\"P(\"&A4&\")\"","v":"P(S)"},0.65248226950354615,0.3475177304964539,1]
["W",76,16,{"$f":"SUM(B5:C5)","v":92},null,{"$f":"\"P(\"&A5&\")\"","v":"P(W)"},0.82608695652173914,0.17391304347826086,1]
["Total",{"$f":"SUM(B2:B5)","v":350},{"$f":"SUM(C2:C5)","v":170},{"$f":"SUM(B6:C6)","v":520}]
[]
[]
["a",{"$f":"\"P(wear \"&B1&\") = \"","v":"P(wear DOT-compliant) = "},{"$f":"B6/D6","v":0.67307692307692313}]
["b","Yes, the overall probability has been increasing from .48 five years ago, to .63 one year ago, and is now approximately .67.  The probability that a motorcyclist wears a DOT-compliant helmet appears to be increasing."]
["c","see above"]

{"sheet":"(12)","index":11,"n_rows":11,"n_cols":4,"rows_kept":11,"cut":false,"hidden":false,"merged":[]}
["Powerball",null,null,55]
["Select",5,"numbers from","1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55"]
[null,"Match in any order means COMBIN"]
["and"]
[null,null,null,42]
["Select",1,"numbers from","1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42"]
[]
["a",{"$f":"COMBIN(D1,B2)","v":3478761}," =COMBIN(D1,B2)","Combinations"]
["b",{"$f":"1/B8","v":2.8745866703691342E-7}," =1/B8","Probability to get $200,000"]
["c",{"$f":"B8*D5","v":146107962}," =B8*D5","Total number of combinations * 42 extra "]
[null,{"$f":"1/B10","v":6.8442539770693671E-9}," =1/B10","Probability to win Powerball"]

{"sheet":"(14)","index":12,"n_rows":9,"n_cols":6,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
[null,"E1",{"$f":"\"1/\"&COUNTA($B$1:$B$4)","v":"1/4"},{"$f":"1/COUNTA($B$1:$B$4)","v":0.25},null,"Mutually Exclusive"]
[null,"E2",{"$f":"\"1/\"&COUNTA($B$1:$B$4)","v":"1/4"},{"$f":"1/COUNTA($B$1:$B$4)","v":0.25},null,"Mutually Exclusive"]
[null,"E3",{"$f":"\"1/\"&COUNTA($B$1:$B$4)","v":"1/4"},{"$f":"1/COUNTA($B$1:$B$4)","v":0.25},null,"Mutually Exclusive"]
[null,"E4",{"$f":"\"1/\"&COUNTA($B$1:$B$4)","v":"1/4"},{"$f":"1/COUNTA($B$1:$B$4)","v":0.25},null,"Mutually Exclusive"]
[null,null,null,{"$f":"SUM(D1:D4)","v":1}]
[]
["a","P(E2)",{"$f":"\"1/\"&COUNTA($B$1:$B$4)","v":"1/4"},{"$f":"D2","v":0.25},"simply add because there is no over lap"]
["b","P(E21 or E2)",{"$f":"\"1/\"&COUNTA($B$1:$B$4)&\"+\"&\"1/\"&COUNTA($B$1:$B$4)","v":"1/4+1/4"},{"$f":"SUM(D1:D2)","v":0.5},"simply add because there is no over lap"]
["c","P(E21 or E2 or E4)",{"$f":"\"1/\"&COUNTA($B$1:$B$4)&\"+1/\"&COUNTA($B$1:$B$4)&\"+1/\"&COUNTA($B$1:$B$4)","v":"1/4+1/4+1/4"},{"$f":"SUM(D1:D2,D4)","v":0.75},"simply add because there is no over lap"]

{"sheet":"(15)","index":13,"n_rows":53,"n_cols":9,"rows_kept":53,"cut":false,"hidden":false,"merged":[]}
["Cards","Probability",null,"Count",null,"Samples Points for Ace","Samples Points for Club","Samples Points for Face Card"]
["Club 1",{"$f":"1/$D$2","v":1.9230769230769232E-2},null,{"$f":"COUNTA(A2:A53)","v":52},null,{"$f":"A14","v":"Club A"},{"$f":"A2","v":"Club 1"},{"$f":"A11","v":"Club J"}]
["Club 2",1.9230769230769232E-2,null,null,null,{"$f":"A27","v":"Diamond A"},{"$f":"A3","v":"Club 2"},{"$f":"A12","v":"Club Q"}]
["Club 3",1.9230769230769232E-2,null,null,null,{"$f":"A40","v":"Spade A"},"Club 3",{"$f":"A13","v":"Club K"}]
["Club 4",1.9230769230769232E-2,null,null,null,{"$f":"A53","v":"Heart A"},"Club 4",{"$f":"A24","v":"Diamond J"}]
["Club 5",1.9230769230769232E-2,null,null,null,null,"Club 5",{"$f":"A25","v":"Diamond Q"}]
["Club 6",1.9230769230769232E-2,null,null,null,null,"Club 6",{"$f":"A26","v":"Diamond K"}]
["Club 7",1.9230769230769232E-2,null,null,null,null,"Club 7",{"$f":"A37","v":"Spade J"}]
["Club 8",1.9230769230769232E-2,null,null,null,null,"Club 8",{"$f":"A38","v":"Spade Q"}]
["Club 9",1.9230769230769232E-2,null,null,null,null,"Club 9",{"$f":"A39","v":"Spade K"}]
["Club J",1.9230769230769232E-2,null,null,null,null,"Club J",{"$f":"A50","v":"Heart J"}]
["Club Q",1.9230769230769232E-2,null,null,null,null,"Club Q",{"$f":"A51","v":"Heart Q"}]
["Club K",1.9230769230769232E-2,null,null,null,null,"Club K",{"$f":"A52","v":"Heart K"}]
["Club A",1.9230769230769232E-2,null,null,null,null,"Club A"]
["Diamond 1",1.9230769230769232E-2]
["Diamond 2",1.9230769230769232E-2]
["Diamond 3",1.9230769230769232E-2,null,null,null,"Count","Count","Count","Use COUNTA function to count words"]
["Diamond 4",1.9230769230769232E-2,null,null,null,{"$f":"COUNTA(F2:F16)","v":4},{"$f":"COUNTA(G2:G16)","v":13},{"$f":"COUNTA(H2:H16)","v":12}]
["Diamond 5",1.9230769230769232E-2,null,null,null,"P(pull an Ace)","P(Pull A Club)","P(Pull Face Card)"]
["Diamond 6",1.9230769230769232E-2,null,null,null,{"$f":"COUNTA(F2:F16)&\"/\"&$D$2","v":"4/52"},{"$f":"COUNTA(G2:G16)&\"/\"&$D$2","v":"13/52"},{"$f":"COUNTA(H2:H16)&\"/\"&$D$2","v":"12/52"}]
["Diamond 7",1.9230769230769232E-2,null,null,null,{"$f":"F18/$D$2","v":7.6923076923076927E-2},{"$f":"G18/$D$2","v":0.25},{"$f":"H18/$D$2","v":0.23076923076923078}]
["Diamond 8",1.9230769230769232E-2]
["Diamond 9",1.9230769230769232E-2]
["Diamond J",1.9230769230769232E-2]
["Diamond Q",1.9230769230769232E-2]
["Diamond K",1.9230769230769232E-2]
["Diamond A",1.9230769230769232E-2]
["Spade 1",1.9230769230769232E-2,null,null,null,"check","check","check"]
["Spade 2",1.9230769230769232E-2,null,null,null,{"$f":"COUNTA(F2:F16)/$D$2","v":7.6923076923076927E-2},{"$f":"COUNTA(G2:G16)/$D$2","v":0.25},{"$f":"COUNTA(H2:H16)/$D$2","v":0.23076923076923078}]
["Spade 3",1.9230769230769232E-2,null,null,null,{"$f":"SUMPRODUCT(SUMIF($A$2:$A$53,F2:F16,$B$2:$B$53))","v":7.6923076923076927E-2},{"$f":"SUMPRODUCT(SUMIF($A$2:$A$53,G2:G16,$B$2:$B$53))","v":0.24999999999999994},{"$f":"SUMPRODUCT(SUMIF($A$2:$A$53,H2:H16,$B$2:$B$53))","v":0.23076923076923073}]
["Spade 4",1.9230769230769232E-2]
["Spade 5",1.9230769230769232E-2]
["Spade 6",1.9230769230769232E-2]
["Spade 7",{"$f":"1/$D$2","v":1.9230769230769232E-2}]
["Spade 8",1.9230769230769232E-2]
["Spade 9",1.9230769230769232E-2]
["Spade J",1.9230769230769232E-2]
["Spade Q",1.9230769230769232E-2]
["Spade K",1.9230769230769232E-2]
["Spade A",1.9230769230769232E-2]
["Heart 1",1.9230769230769232E-2]
["Heart 2",1.9230769230769232E-2]
["Heart 3",1.9230769230769232E-2]
["Heart 4",1.9230769230769232E-2]
["Heart 5",1.9230769230769232E-2]
["Heart 6",1.9230769230769232E-2]
["Heart 7",1.9230769230769232E-2]
["Heart 8",1.9230769230769232E-2]
["Heart 9",1.9230769230769232E-2]
["Heart J",1.9230769230769232E-2]
["Heart Q",1.9230769230769232E-2]
["Heart K",1.9230769230769232E-2]
["Heart A",1.9230769230769232E-2]

{"sheet":"(16)","index":14,"n_rows":37,"n_cols":17,"rows_kept":37,"cut":false,"hidden":false,"merged":[[7,2,12,2]]}
[null,"# of Steps or Trials =","Roll dice once with two die",2,null,null,null,null,null,null,"b","Die 1","Die 2","Sample Point","SUM",null,"check"]
[null,"Possible outcomes from one die",6,null,null,null,null,null,null,null,null,1,{"$f":"MOD(ROWS(M$2:M2)-1,6)+1","v":1},{"$f":"\"(\"&L2&\", \"&M2&\")\"","v":"(1, 1)"},{"$f":"SUM(L2:M2)","v":2},null,{"$f":"SUM(O2:O37)=SUM(E8:J13)","v":true}]
["a","Possible outcomes from two dice",{"$f":"C2&\"*\"&C2&\" = \"&C2*C2","v":"6*6 = 36"},{"$f":"C2*C2","v":36},null,null,null,null,null,null,null,1,{"$f":"MOD(ROWS(M$2:M3)-1,6)+1","v":2},{"$f":"\"(\"&L3&\", \"&M3&\")\"","v":"(1, 2)"},{"$f":"SUM(L3:M3)","v":3}]
[null,null,null,null,null,null,null,null,null,null,null,1,{"$f":"MOD(ROWS(M$2:M4)-1,6)+1","v":3},"(1, 3)",4]
[null,"b","Sum of each possibility",null,null,null,null,null,null,null,null,1,{"$f":"MOD(ROWS(M$2:M5)-1,6)+1","v":4},"(1, 4)",5]
[null,null,null,null,"Die 2",null,null,null,null,null,null,1,{"$f":"MOD(ROWS(M$2:M6)-1,6)+1","v":5},"(1, 5)",6]
[null,null,null,null,1,2,3,4,5,6,null,1,{"$f":"MOD(ROWS(M$2:M7)-1,6)+1","v":6},"(1, 6)",7]
[null,null,"Die 1",1,{"$f":"E$7+$D8","v":2},3,4,5,6,7,null,2,{"$f":"MOD(ROWS(M$2:M8)-1,6)+1","v":1},"(2, 1)",3]
[null,null,null,2,3,4,5,6,7,8,null,2,{"$f":"MOD(ROWS(M$2:M9)-1,6)+1","v":2},"(2, 2)",4]
[null,null,null,3,4,5,6,7,8,9,null,2,{"$f":"MOD(ROWS(M$2:M10)-1,6)+1","v":3},"(2, 3)",5]
[null,null,null,4,5,6,7,8,9,10,null,2,{"$f":"MOD(ROWS(M$2:M11)-1,6)+1","v":4},"(2, 4)",6]
[null,null,null,5,6,7,8,9,10,11,null,2,{"$f":"MOD(ROWS(M$2:M12)-1,6)+1","v":5},"(2, 5)",7]
[null,null,null,6,7,8,9,10,11,12,null,2,{"$f":"MOD(ROWS(M$2:M13)-1,6)+1","v":6},"(2, 6)",8]
[null,null,null,null,null,null,null,null,null,null,null,3,{"$f":"MOD(ROWS(M$2:M14)-1,6)+1","v":1},"(3, 1)",4]
[null,"c",7,{"$f":"\"P(=\"&C15&\")\"","v":"P(=7)"},{"$f":"COUNTIF($E$8:$J$13,C15)&\"/\"&$D$3","v":"6/36"},{"$f":"COUNTIF($E$8:$J$13,C15)/$D$3","v":0.16666666666666666},null,null,null,null,null,3,{"$f":"MOD(ROWS(M$2:M15)-1,6)+1","v":2},"(3, 2)",5]
[null,"d",9,{"$f":"\"P(>=\"&C16&\")\"","v":"P(>=9)"},{"$f":"COUNTIF($E$8:$J$13,\">=\"&C16)&\"/\"&$D$3","v":"10/36"},{"$f":"COUNTIF($E$8:$J$13,\">=\"&C16)/$D$3","v":0.27777777777777779},null,null,null,null,null,3,{"$f":"MOD(ROWS(M$2:M16)-1,6)+1","v":3},"(3, 3)",6]
[null,"e","Count Odd",{"$f":"D3/2","v":18},null,null,null,null,null,null,null,3,{"$f":"MOD(ROWS(M$2:M17)-1,6)+1","v":4},"(3, 4)",7]
[null,null,"Count Even",{"$f":"D3/2","v":18},null,null,null,null,null,null,null,3,{"$f":"MOD(ROWS(M$2:M18)-1,6)+1","v":5},"(3, 5)",8]
[null,{"$f":"\"I do not agree because there are \"&D24&\" odd numbers and \"&D25&\" even numbers.\"","v":"I do not agree because there are 18 odd numbers and 18 even numbers."},null,null,null,null,null,null,null,null,null,3,{"$f":"MOD(ROWS(M$2:M19)-1,6)+1","v":6},"(3, 6)",9]
[null,null,null,null,null,null,null,null,null,null,null,4,{"$f":"MOD(ROWS(M$2:M20)-1,6)+1","v":1},"(4, 1)",5]
[null,"f","Classical",null,null,null,null,null,null,null,null,4,{"$f":"MOD(ROWS(M$2:M21)-1,6)+1","v":2},"(4, 2)",6]
[null,null,{"$f":"\"1/\"&D3&\" for each sample point\"","v":"1/36 for each sample point"},null,null,null,null,null,null,null,null,4,{"$f":"MOD(ROWS(M$2:M22)-1,6)+1","v":3},"(4, 3)",7]
[null,null,null,null,null,null,null,null,null,null,null,4,{"$f":"MOD(ROWS(M$2:M23)-1,6)+1","v":4},"(4, 4)",8]
[null,null,"check",{"$f":"D3-SUMPRODUCT(--(MOD($E$8:$J$13,2)=0))","v":18},null,null,null,null,null,null,null,4,{"$f":"MOD(ROWS(M$2:M24)-1,6)+1","v":5},"(4, 5)",9]
[null,null,null,{"$f":"SUMPRODUCT(--(MOD($E$8:$J$13,2)=0))","v":18},null,null,null,null,null,null,null,4,{"$f":"MOD(ROWS(M$2:M25)-1,6)+1","v":6},"(4, 6)",10]
[null,null,null,null,null,null,null,null,null,null,null,5,{"$f":"MOD(ROWS(M$2:M26)-1,6)+1","v":1},"(5, 1)",6]
[null,null,null,null,null,null,null,null,null,null,null,5,{"$f":"MOD(ROWS(M$2:M27)-1,6)+1","v":2},"(5, 2)",7]
[null,null,null,null,null,null,null,null,null,null,null,5,{"$f":"MOD(ROWS(M$2:M28)-1,6)+1","v":3},"(5, 3)",8]
[null,null,null,null,null,null,null,null,null,null,null,5,{"$f":"MOD(ROWS(M$2:M29)-1,6)+1","v":4},"(5, 4)",9]
[null,null,null,null,null,null,null,null,null,null,null,5,{"$f":"MOD(ROWS(M$2:M30)-1,6)+1","v":5},"(5, 5)",10]
[null,null,null,null,null,null,null,null,null,null,null,5,{"$f":"MOD(ROWS(M$2:M31)-1,6)+1","v":6},"(5, 6)",11]
[null,null,null,null,null,null,null,null,null,null,null,6,{"$f":"MOD(ROWS(M$2:M32)-1,6)+1","v":1},"(6, 1)",7]
[null,null,null,null,null,null,null,null,null,null,null,6,{"$f":"MOD(ROWS(M$2:M33)-1,6)+1","v":2},"(6, 2)",8]
[null,null,null,null,null,null,null,null,null,null,null,6,{"$f":"MOD(ROWS(M$2:M34)-1,6)+1","v":3},"(6, 3)",9]
[null,null,null,null,null,null,null,null,null,null,null,6,{"$f":"MOD(ROWS(M$2:M35)-1,6)+1","v":4},"(6, 4)",10]
[null,null,null,null,null,null,null,null,null,null,null,6,{"$f":"MOD(ROWS(M$2:M36)-1,6)+1","v":5},"(6, 5)",11]
[null,null,null,null,null,null,null,null,null,null,null,6,{"$f":"MOD(ROWS(M$2:M37)-1,6)+1","v":6},"(6, 6)",12]

{"sheet":"(18)","index":15,"n_rows":14,"n_cols":11,"rows_kept":14,"cut":false,"hidden":false,"merged":[]}
["Number of Family Meals","Number Of Times Outcomes Occurred","Probability"]
[0,11,{"$f":"B2/$B$10","v":2.2177419354838711E-2}]
[1,11,2.2177419354838711E-2]
[2,30,6.0483870967741937E-2]
[3,36,7.2580645161290328E-2]
[4,36,7.2580645161290328E-2]
[5,119,0.23991935483870969]
[6,114,0.22983870967741934]
[7,139,0.28024193548387094]
["Total",{"$f":"SUM(B2:B9)","v":496},{"$f":"SUM(C2:C9)","v":1}]
[null,null,null,null,null,"Method 1",null,"Method 2",null,null,"Method 3"]
["a","Exactly",0,{"$f":"B12&\" \"&C12&\" meals\"","v":"Exactly 0 meals"},{"$f":"\"P(\"&D12&\") =\"","v":"P(Exactly 0 meals) ="},{"$f":"C2","v":2.2177419354838711E-2},null,{"$f":"SUMIF($A$2:$A$9,C12,$B$2:$B$9)&\"/\"&$B$10","v":"11/496"},{"$f":"SUMIF($A$2:$A$9,C12,$B$2:$B$9)/$B$10","v":2.2177419354838711E-2},null,{"$f":"SUMIF($A$2:$A$9,C12,$C$2:$C$9)","v":2.2177419354838711E-2}]
["b","At least",4,{"$f":"B13&\" \"&C13&\" meals\"","v":"At least 4 meals"},{"$f":"\"P(\"&D13&\") =\"","v":"P(At least 4 meals) ="},{"$f":"SUM(C6:C9)","v":0.82258064516129026},null,{"$f":"SUMIF($A$2:$A$9,\">=\"&C13,$B$2:$B$9)&\"/\"&$B$10","v":"408/496"},{"$f":"SUMIF($A$2:$A$9,\">=\"&C13,$B$2:$B$9)/$B$10","v":0.82258064516129037},null,{"$f":"SUMIF($A$2:$A$9,\">=\"&C13,$C$2:$C$9)","v":0.82258064516129026}]
["c","At most",2,{"$f":"B14&\" \"&C14&\" meals\"","v":"At most 2 meals"},{"$f":"\"P(\"&D14&\") =\"","v":"P(At most 2 meals) ="},{"$f":"SUM(C2:C4)","v":0.10483870967741936},null,{"$f":"SUMIF($A$2:$A$9,\"<=\"&C14,$B$2:$B$9)&\"/\"&$B$10","v":"52/496"},{"$f":"SUMIF($A$2:$A$9,\"<=\"&C14,$B$2:$B$9)/$B$10","v":0.10483870967741936},null,{"$f":"SUMIF($A$2:$A$9,\"<=\"&C14,$C$2:$C$9)","v":0.10483870967741936}]

{"sheet":"(19)","index":16,"n_rows":13,"n_cols":4,"rows_kept":13,"cut":false,"hidden":true,"merged":[]}
[null,"Participatants in Millions"]
["Activity","Male",null,"Female"]
["Bicycle",22.2,null,21]
["Camp",25.6,null,24.3]
["Walk",28.7,null,57.5]
["Equip",20.399999999999999,null,24.4]
["Swim",26.4,null,34.4]
[null,{"$f":"SUM(B3:B7)","v":123.30000000000001},null,{"$f":"SUM(D3:D7)","v":161.6}]
[]
["7 years or older"]
["Male",120.9]
["Female",127.6]
["Total Population in age group",{"$f":"SUM(B11:B12)","v":248.5}]

{"sheet":"(21)","index":17,"n_rows":13,"n_cols":7,"rows_kept":13,"cut":false,"hidden":false,"merged":[]}
[null,null,"in millions"]
[null,null,"Age","Number","P(x)"]
[18,24,{"$f":"A3&\"-\"&B3","v":"18-24"},29.8,{"$f":"D3/$D$9","v":0.13093145869947276}]
[{"$f":"B3+1","v":25},{"$f":"A4+9","v":34},{"$f":"A4&\"-\"&B4","v":"25-34"},40,0.17574692442882248]
[{"$f":"B4+1","v":35},44,{"$f":"A5&\"-\"&B5","v":"35-44"},43.4,0.19068541300527239]
[45,54,{"$f":"A6&\"-\"&B6","v":"45-54"},43.9,0.19288224956063266]
[55,64,{"$f":"A7&\"-\"&B7","v":"55-64"},32.700000000000003,0.14367311072056238]
[65,null,{"$f":"A8","v":65},37.799999999999997,0.16608084358523723]
[null,null,"Total",{"$f":"SUM(D3:D8)","v":227.60000000000002},{"$f":"SUM(E3:E8)","v":1}]
[]
[null,"a",{"$f":"\"P(\"&A3&\" to \"&B3&\")\"","v":"P(18 to 24)"},{"$f":"D3/D9","v":0.13093145869947276},{"$f":"D3&\"/\"&$D$9","v":"29.8/227.6"},null,{"$f":"E3","v":0.13093145869947276}]
[null,"b",{"$f":"\"P(\"&A3&\" to \"&B4&\")\"","v":"P(18 to 34)"},{"$f":"SUM(D3:D4)/D9","v":0.30667838312829521},{"$f":"\"(\"&D3&\"+\"&D4&\")/\"&$D$9","v":"(29.8+40)/227.6"},"or",{"$f":"SUM(E3:E4)","v":0.30667838312829521}]
[null,"c","P(45 or more)",{"$f":"SUM(D6:D8)/D9","v":0.50263620386643226},{"$f":"\"(\"&D6&\"+\"&D7&\"+\"&D8&\")/\"&$D$9","v":"(43.9+32.7+37.8)/227.6"},null,{"$f":"SUM(E6:E8)","v":0.50263620386643226}]

{"sheet":"(22)","index":18,"n_rows":48,"n_cols":8,"rows_kept":48,"cut":false,"hidden":false,"merged":[[5,4,9,4]]}
[null,"Ei = Experimental Outcome = Sample Point"]
[null,"Each Ei has an equally likely chance of occurring"]
[null,"Event = 1 or more Sample Points"]
[]
[null,null,null,"Sample Space",null,"P(Ei) = Probability for each Sample Point"]
[null,null,null,"E1","Sample Points",{"$f":"\"P(\"&D6&\")\"","v":"P(E1)"},{"$f":"1/COUNTA($D$6:$D$10)","v":0.2}]
[null,null,null,"E2",null,{"$f":"\"P(\"&D7&\")\"","v":"P(E2)"},{"$f":"1/COUNTA($D$6:$D$10)","v":0.2}]
[null,null,null,"E3",null,{"$f":"\"P(\"&D8&\")\"","v":"P(E3)"},{"$f":"1/COUNTA($D$6:$D$10)","v":0.2}]
[null,null,null,"E4",null,{"$f":"\"P(\"&D9&\")\"","v":"P(E4)"},{"$f":"1/COUNTA($D$6:$D$10)","v":0.2}]
[null,null,null,"E5",null,{"$f":"\"P(\"&D10&\")\"","v":"P(E5)"},{"$f":"1/COUNTA($D$6:$D$10)","v":0.2}]
[]
[null,"Count Equally Likely Sample Points",null,null,{"$f":"COUNTA(D6:D10)","v":5}]
[]
[null,"Event Notation","Event","Sample Points in Event","P(Event)","# of Equally Likely Sample Points","Probability for Each Event\nSUM of Sample Points (Union or Intersection, use appropriate rule)","Since Each is equally likely, P(Ei) = FavorableOutcome/TotalOutcomes"]
["a","A",{"$f":"\"Event \"&B15&\" =\"","v":"Event A ="},{"$f":"\"{\"&D6&\", \"&D7&\"}\"","v":"{E1, E2}"},{"$f":"F6&\" + \"&F7","v":"P(E1) + P(E2)"},2,{"$f":"SUM(G6:G7)","v":0.4},{"$f":"F15/$E$12","v":0.4}]
["a","B",{"$f":"\"Event \"&B16&\" =\"","v":"Event B ="},{"$f":"\"{\"&D8&\", \"&D9&\"}\"","v":"{E3, E4}"},{"$f":"F8&\" + \"&F9","v":"P(E3) + P(E4)"},2,{"$f":"SUM(G8:G9)","v":0.4},{"$f":"F16/$E$12","v":0.4}]
["a","C",{"$f":"\"Event \"&B17&\" =\"","v":"Event C ="},{"$f":"\"{\"&D7&\", \"&D8&\", \"&D10&\"}\"","v":"{E2, E3, E5}"},{"$f":"F7&\" + \"&F8&\" + \"&F10","v":"P(E2) + P(E3) + P(E5)"},3,{"$f":"SUM(G7:G8,G10)","v":0.60000000000000009},{"$f":"F17/$E$12","v":0.6}]
[]
["b","Yes, A and B are Mutually Exclusive because they do not share any sample points"]
["b",{"$f":"\"P(\"&B15&\" U \"&B16&\") = \"&E15&\" + \"&E16","v":"P(A U B) = P(E1) + P(E2) + P(E3) + P(E4)"},null,null,{"$f":"SUM(G15:G16)","v":0.8}]
[]
["c","Not Event A = Ac =",null,{"$f":"\"{\"&D8&\", \"&D9&\", \"&D10&\"}\"","v":"{E3, E4, E5}"}]
["c","Not Event C = Cc =",null,{"$f":"\"{\"&D6&\", \"&D7&\"}\"","v":"{E1, E2}"}]
["c","P(Ac)",{"$f":"SUM(G8:G10)","v":0.60000000000000009}]
["c","P(Cc)",{"$f":"SUM(G6:G7)","v":0.4}]
[]
["d","A Union Not B = A U Bc",null,{"$f":"C29","v":"{E1, E2, E5}"}]
[null,{"$f":"C15","v":"Event A ="},{"$f":"D15","v":"{E1, E2}"}]
[null,"Event Bc =",{"$f":"\"{\"&D6&\", \"&D7&\", \"&D10&\"}\"","v":"{E1, E2, E5}"}]
["d",{"$f":"\"P(A U Bc) = \"&F6&\" + \"&F7&\" + \"&F10","v":"P(A U Bc) = P(E1) + P(E2) + P(E5)"},null,{"$f":"SUM(G6:G7,G10)","v":0.60000000000000009}]
[]
["e",{"$f":"\"P(B U C) = \"&D33&\" + \"&D34&\" - \"&F8&\" = \"&F8&\" + \"&F9&\" + \"&F7&\" + \"&F10","v":"P(B U C) = P(E3) + P(E4) + P(E2) + P(E3) + P(E5) - P(E3) = P(E3) + P(E4) + P(E2) + P(E5)"},null,null,null,{"$f":"SUM(G7:G10)","v":0.8}]
[null,{"$f":"C16","v":"Event B ="},"{E3, E4}","P(E3) + P(E4)"]
[null,"Event C =","{E2, E3, E5}","P(E2) + P(E3) + P(E5)"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Alternative Method for a"]
[null,"Event Notation","Event","Sample Point",null,null,"Sample Points in Event","Probability for Each Event\nSUM of Sample Points (Union or Intersection, use appropriate rule)"]
[null,"A",{"$f":"\"Event \"&B46&\" =\"","v":"Event A ="},{"$f":"$D$6","v":"E1"},{"$f":"$D$7","v":"E2"},null,{"$f":"\"{\"&D46&\", \"&E46&\"}\"","v":"{E1, E2}"},{"$f":"SUMPRODUCT(SUMIF($D$6:$D$10,D46:F46,$G$6:$G$10))","v":0.4}]
[null,"B",{"$f":"\"Event \"&B47&\" =\"","v":"Event B ="},{"$f":"$D$8","v":"E3"},{"$f":"$D$9","v":"E4"},null,{"$f":"\"{\"&D47&\", \"&E47&\"}\"","v":"{E3, E4}"},{"$f":"SUMPRODUCT(SUMIF($D$6:$D$10,D47:F47,$G$6:$G$10))","v":0.4}]
[null,"C",{"$f":"\"Event \"&B48&\" =\"","v":"Event C ="},{"$f":"$D$7","v":"E2"},{"$f":"$D$8","v":"E3"},{"$f":"$D$10","v":"E5"},{"$f":"\"{\"&D48&\", \"&E48&\", \"&F48&\"}\"","v":"{E2, E3, E5}"},{"$f":"SUMPRODUCT(SUMIF($D$6:$D$10,D48:F48,$G$6:$G$10))","v":0.60000000000000009}]

{"sheet":"(23)","index":19,"n_rows":25,"n_cols":12,"rows_kept":25,"cut":false,"hidden":false,"merged":[]}
[null,"E1",{"$f":"\"P(\"&B1&\")\"","v":"P(E1)"},0.05]
[null,"E2",{"$f":"\"P(\"&B2&\")\"","v":"P(E2)"},0.2]
[null,"E3","P(E3)",0.2]
[null,"E4","P(E4)",0.25]
[null,"E5","P(E5)",0.15]
[null,"E6","P(E6)",0.1]
[null,"E7","P(E7)",0.05]
[null,null,null,{"$f":"SUM(D1:D7)","v":1}]
[]
[null,"Event"]
["a","A",{"$f":"\"P(\"&B11&\")\"","v":"P(A)"},{"$f":"\"{\"&B1&\", \"&B4&\", \"&B6&\"}\"","v":"{E1, E4, E6}"},{"$f":"\"P(\"&SUBSTITUTE(SUBSTITUTE(D11,\"{\",\"\"),\"}\",\"\")&\")\"","v":"P(E1, E4, E6)"},{"$f":"SUM(D1,D4,D6)","v":0.4}]
["a","B",{"$f":"\"P(\"&B12&\")\"","v":"P(B)"},{"$f":"\"{\"&B2&\", \"&B4&\", \"&B7&\"}\"","v":"{E2, E4, E7}"},{"$f":"\"P(\"&SUBSTITUTE(SUBSTITUTE(D12,\"{\",\"\"),\"}\",\"\")&\")\"","v":"P(E2, E4, E7)"},{"$f":"SUM(D2,D4,D7)","v":0.5}]
["a","C",{"$f":"\"P(\"&B13&\")\"","v":"P(C)"},{"$f":"\"{\"&B2&\", \"&B3&\", \"&B5&\", \"&B7&\"}\"","v":"{E2, E3, E5, E7}"},{"$f":"\"P(\"&SUBSTITUTE(SUBSTITUTE(D13,\"{\",\"\"),\"}\",\"\")&\")\"","v":"P(E2, E3, E5, E7)"},{"$f":"SUM(D2:D3,D5,D7)","v":0.60000000000000009}]
[]
["b","A U B =",{"$f":"\"{\"&B1&\", \"&B4&\", \"&B6&\", \"&B2&\", \"&B7&\"}\"","v":"{E1, E4, E6, E2, E7}"}]
["b","P(A U B) =",{"$f":"SUM(D1,D4,D6,D2,D7)","v":0.65000000000000013}]
[]
["c","A ∩ B =",{"$f":"B4","v":"E4"}]
["c","P(A ∩ B) =",{"$f":"D4","v":0.25}]
[]
["d","Yes, A and C are mutually exclusive because they have no sample points in common"]
[]
["e","Bc",{"$f":"\"{\"&B1&\", \"&B3&\", \"&B5&\", \"&B6&\"}\"","v":"{E1, E3, E5, E6}"}]
[null,"P(Bc)",{"$f":"SUM(D1,D3,D5:D6)","v":0.5}]
[null,null,{"$f":"SUMPRODUCT(SUMIF(B1:B7,I25:L25,D1:D7))","v":0.5},null,null,null,null,null,"E1","E3","E5","E6"]

{"sheet":"(25)","index":20,"n_rows":9,"n_cols":7,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
[null,"Young Adults = 18 - 24 years old"]
[null,"Female lives at home","F",{"$f":"\"P(\"&C2&\")\"","v":"P(F)"},0.42]
[null,"Male lives at home","M",{"$f":"\"P(\"&C3&\")\"","v":"P(M)"},0.56000000000000005]
[null,"F ∩ M","F and M",{"$f":"\"P(\"&C4&\")\"","v":"P(F and M)"},0.24,"Intersection = And = ∩ = and = both = joint = concurrent"]
[null,null,null,null,null,"Remember to not double count when you do a Union = U = OR = at least 1"]
[null,"Randomly Select a Male and a Female:"]
["a","P(at least 1 of the 2 selected lives at home) =\n(this means 1 or more)",{"$f":"D2&\" + \"&D3&\" - \"&D4&CHAR(10)&\"(subtract because we don't want to Double Count)\"","v":"P(F) + P(M) - P(F and M)\n(subtract because we don't want to Double Count)"},null,null,{"$f":"E2&\" + \"&E3&\" - \"&E4","v":"0.42 + 0.56 - 0.24"},{"$f":"E2+E3-E4","v":0.74}]
[]
["b","P(Neither Live At Home)\n(if we know the probability that 1 or more live at home, then 1 - P(1 or more) = P(None) = P(Neither)",{"$f":"1-G7","v":0.26}]

{"sheet":"(27old)","index":21,"n_rows":18,"n_cols":13,"rows_kept":18,"cut":false,"hidden":true,"merged":[[7,3,9,3]]}
[null,"Big Ten in Rose Bowl",null,2961]
[null,"Pac-10 in Rose Bowl",null,4494]
[null,"Neither in Rose Bowl",null,6823]
[null,"Total Respondents",null,13429]
[]
[null,null,null,null,null,"Big Ten"]
[null,null,null,null,null,"Yes","No","Total",null,null,"check"]
[null,null,null,"Pac-10","Yes",{"$f":"H8-G8","v":849},{"$f":"G10-G9","v":3645},{"$f":"D2","v":4494},null,null,{"$f":"F8","v":849},{"$f":"G8","v":3645},{"$f":"SUM(K8:L8)","v":4494}]
[null,null,null,null,"No",{"$f":"F10-F8","v":2112},{"$f":"D3","v":6823},{"$f":"H10-H8","v":8935},null,null,{"$f":"F9","v":2112},{"$f":"G9","v":6823},{"$f":"SUM(K9:L9)","v":8935}]
[null,null,null,null,"Total",{"$f":"D1","v":2961},{"$f":"H10-F10","v":10468},{"$f":"D4","v":13429},null,null,{"$f":"SUM(K8:K9)","v":2961},{"$f":"SUM(L8:L9)","v":10468},{"$f":"SUM(K10:L10)","v":13429}]
[]
[null,null,null,null,"Steps to Set Up This Table this:"]
[null,null,null,null,1,"Place numbers in white cells"]
[null,null,null,null,2,{"$f":"\"Solve for value in cell \"&ADDRESS(ROW(H9),COLUMN(H9),4)&\" with the formula \"&H10&\"-\"&H8&\" = \"&H10-H8","v":"Solve for value in cell H9 with the formula 13429-4494 = 8935"}]
[null,null,null,null,3,{"$f":"\"Solve for value in cell \"&ADDRESS(ROW(G10),COLUMN(G10),4)&\" with the formula \"&H10&\"-\"&F10&\" = \"&G10-G8","v":"Solve for value in cell G10 with the formula 13429-2961 = 6823"}]
["a","P(Neither in Rose Bowl)",{"$f":"G9/H10","v":0.50807952937672207},null,4,{"$f":"\"Solve for value in cell \"&ADDRESS(ROW(G8),COLUMN(G8),4)&\" with the formula \"&G10&\"-\"&G9&\" = \"&G10-G9","v":"Solve for value in cell G8 with the formula 10468-6823 = 3645"}]
["b","P(Either)\nP(1 or the other will be in Rose Bowl) = P(Big Ten or Pac-10 or Both) =",{"$f":"SUM(F10,H8,-F8)/H10","v":0.49192047062327798},null,5,{"$f":"\"Solve for value in cell \"&ADDRESS(ROW(F8),COLUMN(F8),4)&\" with the formula \"&H8&\"-\"&G8&\" = \"&H8-G8","v":"Solve for value in cell F8 with the formula 4494-3645 = 849"}]
["c","P(Both)\nP(Pac-10 AND Big Ten)\nP(Pac-10 ∩ Big Ten)",{"$f":"F8/H10","v":6.3221386551493036E-2},null,6,{"$f":"\"Solve for value in cell \"&ADDRESS(ROW(F9),COLUMN(F9),4)&\" with the formula \"&F10&\"-\"&F8&\" = \"&F10-F8","v":"Solve for value in cell F9 with the formula 2961-849 = 2112"}]

{"sheet":"(28)","index":22,"n_rows":6,"n_cols":3,"rows_kept":6,"cut":false,"hidden":false,"merged":[]}
["P(Rented car over last 12 months for business)",0.45800000000000002]
["P(Rented car over last 12 months for personal)",0.54]
["P(Rented car over last 12 months for Business AND Personal)\nP(Rented car over last 12 months for Business ∩ Personal)",0.3,"Remember to not double count when you do a Union = U = OR = at least 1"]
[]
["P(Rented car over last 12 months for Business OR Personal)",{"$f":"B1+B2-B3","v":0.69799999999999995}]
["P(NOT Rented car over last 12 months for Business OR Personal)",{"$f":"1-B5","v":0.30200000000000005},"P(Neither) = P(None)"]

{"sheet":"(29)","index":23,"n_rows":28,"n_cols":9,"rows_kept":28,"cut":false,"hidden":false,"merged":[]}
["Ivy League","Event Notation","Number","P(x)","P(x)"]
["Early Admit",{"$f":"LEFT(A2,1)","v":"E"},1033,{"$f":"\"P(\"&B2&\")\"","v":"P(E)"},{"$f":"C2/$C$5","v":0.36232900736583656}]
["Reject","R",854,{"$f":"\"P(\"&B3&\")\"","v":"P(R)"},0.29954401964223082]
["Deferred","D",964,"P(D)",0.33812697299193267]
["Total Early Applications Received",null,{"$f":"SUM(C2:C4)","v":2851},null,{"$f":"SUM(E2:E4)","v":1},null,"Early Applications Received",null,2851]
["Past % of deferred that where then admitted in Regular Admissions",null,0.18]
["Total Over Admitted",null,2375]
[]
[]
["a",{"$f":"D2","v":"P(E)"},{"$f":"C2&\"/\"&$C$5","v":"1033/2851"},{"$f":"E2","v":0.36232900736583656}]
[null,"P(R)","854/2851",{"$f":"E3","v":0.29954401964223082}]
[null,"P(D)","964/2851",{"$f":"E4","v":0.33812697299193267}]
[]
["b","Yes, because they share no sample points - no one who was admitted was also deferred."]
["b",{"$f":"\"P(\"&B2&\" and \"&B4&\") = 0\"","v":"P(E and D) = 0"}]
[]
["c","Probability that randomly selected admitted  student was from early group"]
[null,{"$f":"C2&\"/\"&C7","v":"1033/2375"},{"$f":"C2/C7","v":0.43494736842105264}]
[]
["c","Goal: P(In early admission E OR Deferred and Admitted) = P(E OR D-A)"]
[null,"# from deferred group who were latter admitted"]
[null,{"$f":"C4&\" * \"&C6&\" = \"&C4*C6","v":"964 * 0.18 = 173.52"}]
[null,"Event Notation = D-A",{"$f":"C4*C6","v":173.51999999999998}]
[null,"# Early Admit"]
[null,"E",{"$f":"C2","v":1033}]
[null,"Event E and D-A are mutually exclusive"]
[null,"P(E OR D-A)",{"$f":"\"(\"&C23&\" + \"&C2&\")/\"&C5&\" = \"&ROUND(SUM(C2,C23)/C5,4)","v":"(173.52 + 1033)/2851 = 0.4232"}]
[null,null,{"$f":"SUM(C23,C2)/C5","v":0.4231918625043844}]

{"sheet":"(30)","index":24,"n_rows":8,"n_cols":4,"rows_kept":8,"cut":false,"hidden":false,"merged":[]}
[null,"Event","P(Ei)","P(Ei)"]
[null,"A",{"$f":"\"P(\"&B2&\")\"","v":"P(A)"},0.5]
[null,"B",{"$f":"\"P(\"&B3&\")\"","v":"P(B)"},0.6]
[null,{"$f":"B2&\" and \"&B3","v":"A and B"},{"$f":"\"P(\"&B4&\")\"","v":"P(A and B)"},0.4]
[]
["a","P(B|A)",{"$f":"\"= \"&$C$4&\"/\"&C2","v":"= P(A and B)/P(A)"},{"$f":"D4/D3","v":0.66666666666666674}]
["b","P(A|B)",{"$f":"\"= \"&$C$4&\"/\"&C3","v":"= P(A and B)/P(B)"},{"$f":"D4/D2","v":0.8}]
["c","A and B are not independent because P(A) is not equal to P(A|B)"]

{"sheet":"(31)","index":25,"n_rows":10,"n_cols":8,"rows_kept":10,"cut":false,"hidden":false,"merged":[]}
[null,"Event","P(Ei)","P(Ei)"]
[null,"A",{"$f":"\"P(\"&B2&\")\"","v":"P(A)"},0.3,null,"Mutually Exclusive (No Sample Points in common)"]
[null,"B",{"$f":"\"P(\"&B3&\")\"","v":"P(B)"},0.4,null,"Mutually Exclusive (No Sample Points in common)"]
[null,{"$f":"B2&\" and \"&B3","v":"A and B"},"Have no sample points in common"]
[]
["a",{"$f":"\"P(\"&B4&\")\"","v":"P(A and B)"},0]
["b","P(A|B)",{"$f":"C6/D3","v":0}]
["c","Independent means that P(A) = P(A|B), since .3 does not equal 0, they are not independent. Mutually Exclusive means that there are no sample points in common."]
["d","Mutually Exclusive and Independence are not the same. Mutually Exclusive means the two events have no sample points in common and therefore if one event occurs the other cannot occur - the two are dependent in the sense that if one occurs, the other cannot. Independent events are not dependent. Mutually Exclusive events are dependent because P(A) <> P(A|B) and P(A) (nonzero) <> 0."]
[null,null,null,null,null,null,null,"No Overlap"]

{"sheet":"(32-old)","index":26,"n_rows":21,"n_cols":5,"rows_kept":21,"cut":false,"hidden":true,"merged":[]}
[null,null,"Yes","No","Total"]
[null,"18 to 34",750,170,{"$f":"SUM(C2:D2)","v":920}]
[null,"35 and older",950,130,{"$f":"SUM(C3:D3)","v":1080}]
[null,"Total",{"$f":"SUM(C2:C3)","v":1700},{"$f":"SUM(D2:D3)","v":300},{"$f":"SUM(C4:D4)","v":2000}]
[]
["a","Joint Probabilities"]
[null,null,"Yes","No","Total"]
[null,"18 to 34",{"$f":"C2/$E$4","v":0.375},8.5000000000000006E-2,0.46]
[null,"35 and older",0.47499999999999998,6.5000000000000002E-2,0.54]
[null,"Total",0.85,0.15,1]
[]
["b","The majority of people look to be older than 34 (54%) and 46% are 34 or younger."]
[]
["c","P(Not have health insurance) =",{"$f":"D10","v":0.15},"Marginal Probability"]
["d","P(No HI | 18 to 34)",{"$f":"D8/E8","v":0.18478260869565219},"Conditional Probability"]
[null,null,{"$f":"D2/E2","v":0.18478260869565216}]
["e","P(No HI | 35 and older)",{"$f":"D9/E9","v":0.12037037037037036},"Conditional Probability"]
[null,null,{"$f":"D3/E3","v":0.12037037037037036}]
["f","P(18 to 34 | NI)",{"$f":"D8/D10","v":0.56666666666666676},"Conditional Probability"]
[null,null,{"$f":"D2/D4","v":0.56666666666666665}]
["g","85% have health insurance. Given that you are 18 to 34, 18.4% of this group does not have insurance. Given that you are over 34, 12% does not have insurance. Of the no insurance group, about 57% are 18 to 34."]

{"sheet":"(32)","index":27,"n_rows":39,"n_cols":8,"rows_kept":39,"cut":false,"hidden":false,"merged":[]}
["Total Jan Autos sold",657000]
["Down from last jan",0.37]
["Big 3 USA sold",280500,null,"GM","Ford","Chrysler"]
["Down",0.48]
["US non Manufacturers",null,null,"Toyota","Honda","Nissan"]
["Light Truck",null,null,"Pickup","minivan","SUV","Crossover"]
[]
["a",null,"Type of Vehicle"]
[null,null,"Car","Light Truck","Totals"]
["Manufacturer","USA",87400,193100,{"$f":"SUM(C10:D10)","v":280500}]
[null,"Non-USA",228500,148000,{"$f":"SUM(C11:D11)","v":376500}]
[null,"Totals",{"$f":"SUM(C10:C11)","v":315900},{"$f":"SUM(D10:D11)","v":341100},{"$f":"SUM(C12:D12)","v":657000}]
[]
[null,null,"Type of Vehicle"]
[null,null,"Car","Light Truck","Totals",null,"check"]
["Manufacturer","USA",{"$f":"C10/$E$12","v":0.13302891933028918},0.29391171993911719,{"$f":"E10/$E$12","v":0.4269406392694064},null,{"$f":"$E10/$E$12*C10/$E10","v":0.13302891933028918},0.29391171993911719]
[null,"Non-USA",0.34779299847792999,0.22526636225266361,0.5730593607305936,null,0.34779299847792999,0.22526636225266364]
[null,"Totals",{"$f":"C12/$E$12","v":0.4808219178082192},0.51917808219178085,{"$f":"SUM(E16:E17)","v":1}]
[]
["b","There is a higher probability that the vehicle was not manufactured by a U. S. auto maker.  In terms of market share, non U.S. auto makers lead with a 57.3% share of vehicle sales."]
[]
["c","P(Car | USA) = P(Car AND USA) / P(USA)","??"]
[null,"P(Car AND USA)",{"$f":"C16","v":0.13302891933028918}]
[null,"P(USA)",{"$f":"E16","v":0.4269406392694064}]
[null,{"$f":"B22","v":"P(Car | USA) = P(Car AND USA) / P(USA)"},{"$f":"C23/C24","v":0.31158645276292329},"AND/Marginal"]
[]
[null,"P(LT | USA) = P(LT AND USA) / P(USA)","??"]
[null,"P(LT AND USA)",{"$f":"D16","v":0.29391171993911719}]
[null,"P(USA)",{"$f":"E16","v":0.4269406392694064}]
[null,{"$f":"B27","v":"P(LT | USA) = P(LT AND USA) / P(USA)"},{"$f":"C28/C29","v":0.6884135472370766},"AND/Marginal"]
[]
["d","P(Car | Not USA)",{"$f":"C17/E17","v":0.60690571049136788},"AND/Marginal"]
[null,"P(LT | Not USA)",{"$f":"D17/E17","v":0.39309428950863212},"AND/Marginal"]
[]
["e","P(USA | LT) =",{"$f":"D16/D18","v":0.56610964526531804},"AND/Marginal"]
[null,null,"If a vehicle was a light truck, there is better than a 50-50 chance that it was"]
[null,null,"manufactured by one of the U.S. auto makers."]
[]
["f","There is a higher probability, and thus a larger market share for non U.S. auto makers.  However, the U. S. auto makers are leaders in sales for the light truck category."]

{"sheet":"(36)","index":28,"n_rows":30,"n_cols":9,"rows_kept":30,"cut":false,"hidden":false,"merged":[]}
[null,"Made Shots/Taken Shots =",0.89]
[null,"We will assume Independence"]
[]
["a","Attempts taken",2]
[null,"Attempts made",2]
[null,"P(make 2 shots in two tries) =",{"$f":"C1*C1","v":0.79210000000000003}]
[null,"P(make 2 shots in two tries) =",{"$f":"HYPGEOMDIST(C5,C4,89,100)","v":0.79111111111111088},{"$f":"_xlfn.HYPGEOM.DIST(C5,C4,89,100,0)","v":0.79111111111111088}]
[]
["b","P(Miss) = 1 - P(Make it)",{"$f":"1-C1","v":0.10999999999999999}]
[null,"P(None) = P(Miss)*P(Miss) =",{"$f":"C9*C9","v":1.2099999999999998E-2},null,null,"better"]
[null,"P(at least 1) = P(1 or 2) = P(1 U 2) = 1 - P(None) =",{"$f":"1-C10","v":0.9879},null,null,"to"]
[null,"or",null,null,null,"foul"]
[null,{"$f":"\"P(1) + P(2nd single shot) - P(1 and 2 made) = \"&C1&\" + \"&C1&\" - \"&C6&\" =\"","v":"P(1) + P(2nd single shot) - P(1 and 2 made) = 0.89 + 0.89 - 0.7921 ="},{"$f":"C1+C1-C6","v":0.9879},null,null,"center",null,null,{"$f":"C1&\"+\"&C1&\"-\"&C6","v":"0.89+0.89-0.7921"}]
[]
["c","P(Miss) = 1 - P(Make it)",{"$f":"1-C1","v":0.10999999999999999}]
[null,"P(None) = P(Miss)*P(Miss) =",{"$f":"C15*C15","v":1.2099999999999998E-2}]
[null,"or"]
[null,"P(None) = 1 - P(at least 1)",{"$f":"1-C13","v":1.21E-2}]
[]
["d","Made Shots/Taken Shots =",0.57999999999999996]
[null,"We will assume Independence"]
[]
[null,"Attempts taken",2]
[null,"Attempts made",2]
[null,"P(make 2 shots in two tries) =",{"$f":"C20*C20","v":0.33639999999999998}]
[null,"P(make 2 shots in two tries) =",{"$f":"HYPGEOMDIST(C24,C23,58,100)","v":0.33393939393939376},{"$f":"_xlfn.HYPGEOM.DIST(C24,C23,58,100,0)","v":0.33393939393939376}]
[]
[null,"P(Miss) = 1 - P(Make it)",{"$f":"1-C20","v":0.42000000000000004}]
[null,"P(None) = P(Miss)*P(Miss) =",{"$f":"C28*C28","v":0.17640000000000003}]
[null,"P(at least 1) = P(1 or 2) = P(1 U 2) = 1 - P(None) =",{"$f":"1-C29","v":0.8236}]

{"sheet":"(37-old)","index":29,"n_rows":19,"n_cols":8,"rows_kept":19,"cut":false,"hidden":true,"merged":[]}
[null,"P(Use Credit Card)",0.37]
[null,"P(18 to 24 Years old | Use Credit Card)",0.19]
[null,"P(> 24 Years old | Use Credit Card)",0.81]
[null,"Proportion of 18 to 24 who are consumers",0.14000000000000001]
[]
[null,"Proportion of > 24 who are consumers",{"$f":"1-C4","v":0.86},null,null,"18 to 24","> 24","Total"]
[null,"P(Not use CC)",{"$f":"1-C1","v":0.63},null,"Use Credit Card",{"$f":"C2*H7","v":7.0300000000000001E-2},{"$f":"H7-F7","v":0.29969999999999997},0.37]
[null,null,null,null,"Not Use Credit Card",{"$f":"F9-F7","v":6.9700000000000012E-2},{"$f":"G9-G7","v":0.56030000000000002},{"$f":"C7","v":0.63}]
["a","P(Use Credit Card and 18 to 24 Years old)",{"$f":"C2*C1","v":7.0300000000000001E-2},{"$f":"B1&\"*\"&B2&\" = \"&C1&\"*\"&C2","v":"P(Use Credit Card)*P(18 to 24 Years old | Use Credit Card) = 0.37*0.19"},"Total",0.14000000000000001,0.86,{"$f":"SUM(F9:G9)","v":1}]
[null,"P(Use Credit Card | 18 to 24 Years old)",{"$f":"C9/C4","v":0.50214285714285711},{"$f":"B9&\"/\"&B4&\" =\"&CHAR(10)&C9&\"/\"&C4","v":"P(Use Credit Card and 18 to 24 Years old)/Proportion of 18 to 24 who are consumers =\n0.0703/0.14"}]
[]
["b","P(Use Credit Card and > 24 Years old)",{"$f":"C1*C3","v":0.29970000000000002},{"$f":"B1&\"*\"&B3&\" = \"&C1&\"*\"&C3","v":"P(Use Credit Card)*P(> 24 Years old | Use Credit Card) = 0.37*0.81"}]
[null,"P(Use Credit Card | > 24 Years old)",{"$f":"C12/C6","v":0.3484883720930233},{"$f":"B12&\"/\"&B6&\" = \"&C12&\"/\"&C6","v":"P(Use Credit Card and > 24 Years old)/Proportion of > 24 who are consumers = 0.2997/0.86"}]
[]
[]
["c","There is a higher probability that the younger consumer, age 18 to 24, will use plastic when making a purchase. The probability that the 18 to 24 year old consumer uses plastic is .5021 and the probability that the older than 24 year old consumer uses plastic is .3485.  Note that there is greater than .50 probability that the 18 to 24 years old consumer will use plastic."]
["d","Companies such as Visa, Mastercard and Discovery want their cards in the hands of consumers who will have a high probability of using the card.  So yes, these companies should get their cards in the hands of young consumers even before these consumers have established a credit history.  The companies should place a low limit of the amount of credit charges until the young consumer has demonstrated the responsibility to handle higher credit limits.  "]
[]
[null,"Not Assigned"]

{"sheet":"(37)","index":30,"n_rows":31,"n_cols":9,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
["P(Consumer Use Credit Card)",{"$f":"C7","v":"P(C use P)"},0.37]
["P(Consumer 18 to 24 Years old | Use Credit Card)","P(18-24 | C)",0.19]
["P(Consumer > 24 Years old | Use Credit Card)","P(>24 | C)",0.81]
["Proportion of 18 to 24 who are consumers",null,0.14000000000000001]
[]
["Event","Event Notation","P(x)"]
["Event Consumer Used Plasic","C use P",{"$f":"\"P(\"&B7&\")\"","v":"P(C use P)"},0.37,null,"check"]
["Event Consumer Not Used Plasic","C Not use P",{"$f":"\"P(\"&B8&\")\"","v":"P(C Not use P)"},{"$f":"1-D7","v":0.63},null,{"$f":"SUM(D7:D8)","v":1}]
["Event Consumer 18 to 24","C 18 to 24",{"$f":"\"P(\"&B9&\")\"","v":"P(C 18 to 24)"},0.14000000000000001,null,"check"]
["Event Consumer >24","C >24","P(C >24)",{"$f":"1-D9","v":0.86},null,{"$f":"SUM(D9:D10)","v":1}]
[null,null,{"$f":"\"P(\"&B9&\" | \"&B7&\")\"","v":"P(C 18 to 24 | C use P)"},0.19,null,"check"]
[null,null,{"$f":"\"P(\"&B10&\" | \"&B7&\")\"","v":"P(C >24 | C use P)"},0.81,null,{"$f":"SUM(D11:D12)","v":1}]
["Rule =\nP(A AND B) = P(A) * P(B | A)\nP(A) = P(A AND B)/P(B | A)\nP(B | A) = P(A AND B)/P(A)"]
[null,"a",{"$f":"\"P(\"&B7&\" | \"&B9&\")\"","v":"P(C use P | C 18 to 24)"},"??","P(B | A) = P(A AND B)/P(A)"]
[null,null,{"$f":"\"P(\"&B7&\" AND \"&B9&\")\"","v":"P(C use P AND C 18 to 24)"},{"$f":"D7*D11","v":7.0300000000000001E-2},null,null,null,"Check from contingency Table"]
[null,null,{"$f":"C14","v":"P(C use P | C 18 to 24)"},{"$f":"D15/D9","v":0.50214285714285711},null,null,null,{"$f":"C29/C31","v":0.50214285714285711},"AND / Marginal"]
[null,"b",{"$f":"\"P(\"&B7&\" | \"&B10&\")\"","v":"P(C use P | C >24)"},"??","P(A | B) = P(A AND B)/P(B)"]
[null,null,{"$f":"\"P(\"&B7&\" AND \"&B10&\")\"","v":"P(C use P AND C >24)"},{"$f":"D7*D12","v":0.29970000000000002}]
[null,null,{"$f":"C10","v":"P(C >24)"},{"$f":"D10","v":0.86}]
[null,null,{"$f":"C17","v":"P(C use P | C >24)"},{"$f":"D18/D19","v":0.3484883720930233},null,null,null,{"$f":"D29/D31","v":0.3484883720930233},"AND / Marginal"]
[]
[]
[null,"c","There is a higher probability that the younger consumer, age 18 to 24, will use plastic when making a purchase. The probability that the 18 to 24 year old consumer uses plastic is .5021 and the probability that the older than 24 year old consumer uses plastic is .3485.  Note that there is greater than .50 probability that the 18 to 24 years old consumer will use plastic."]
[null,"d","Companies such as Visa, Mastercard and Discovery want their cards in the hands of consumers who will have a high probability of using the card.  So yes, these companies should get their cards in the hands of young consumers even before these consumers have established a credit history.  The companies should place a low limit of the amount of credit charges until the young consumer has demonstrated the responsibility to handle higher credit limits.  "]
[]
[]
[]
[null,null,{"$f":"B9","v":"C 18 to 24"},{"$f":"B10","v":"C >24"}]
[null,{"$f":"B7","v":"C use P"},{"$f":"D7*D11","v":7.0300000000000001E-2},{"$f":"D7*D12","v":0.29970000000000002},{"$f":"SUM(C29:D29)","v":0.37}]
[null,{"$f":"B8","v":"C Not use P"},{"$f":"C31-C29","v":6.9700000000000012E-2},{"$f":"D31-D29","v":0.56030000000000002},{"$f":"SUM(C30:D30)","v":0.63}]
[null,null,{"$f":"D9","v":0.14000000000000001},{"$f":"D10","v":0.86},{"$f":"IF(SUM(E29:E30)=SUM(C31:D31),1,\"\")","v":1}]

{"sheet":"(39)","index":31,"n_rows":9,"n_cols":9,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
["a","**P(A1 AND A2) = 0 ==> means no intersection ==> no sample points in common ==> means Mutually Exclusive"]
[]
[null,"AND = Intersection = upside down U"]
[]
[null,null,null,null,null,null,"b","d"]
["Event","P(x)","Prior Probabilities","P(x)","Conditional Prob","P(x)","Joint Probabilities","P(x)","Posterior Probabilities"]
["A1",{"$f":"\"P(\"&A7&\")\"","v":"P(A1)"},0.4,{"$f":"\"P(B |\"&A7&\")\"","v":"P(B |A1)"},0.2,{"$f":"\"P(\"&A7&\" AND B)\"","v":"P(A1 AND B)"},{"$f":"E7*C7","v":8.0000000000000016E-2},{"$f":"\"P(\"&A7&\" | B)\"","v":"P(A1 | B)"},{"$f":"G7/$G$9","v":0.72727272727272729}]
["A2","P(A2)",0.6,{"$f":"\"P(B |\"&A8&\")\"","v":"P(B |A2)"},0.05,{"$f":"\"P(\"&A8&\" AND B)\"","v":"P(A2 AND B)"},0.03,{"$f":"\"P(\"&A8&\" | B)\"","v":"P(A2 | B)"},0.27272727272727271]
[null,null,{"$f":"SUM(C7:C8)","v":1},null,"c","Total",{"$f":"SUM(G7:G8)","v":0.11000000000000001},"P(B) because Joint Probabilities ((A1 & B) and (A2 & B) are Mutually Exclusive and Union is entire sample space (collectively exhaustive)."]

{"sheet":"(44)","index":32,"n_rows":17,"n_cols":10,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
[null,null,"a",null,"a"]
["Events","P(X)","Prior Prob","P(X)","Conditional Prob","P(X)","Joint Prob","P(X)","Prior Probability"]
["Graduate","P(A1)",0.47,"P(W | A1)",0.5,"P(A1 AND W)",{"$f":"E3*C3","v":0.23499999999999999},"P(A1 | W)",{"$f":"G3/$G$5","v":0.49630411826821536}," << == b"]
["Not Graduate","P(A2)",{"$f":"1-C3","v":0.53},"P(W | A2)",0.45,"P(A2 AND W)",0.23850000000000002,"P(A2 | W)",0.50369588173178459]
[null,null,null,null,"Total","P(W)",{"$f":"SUM(G3:G4)","v":0.47350000000000003},null,{"$f":"SUM(I3:I4)","v":1}]
[]
[null,null,null,null,null,null,"**P(W) because Joint Probabilities ((A1 & W) and (A2 & W) are Mutually Exclusive and Union is entire sample space (collectively exhaustive)."]
["c"]
["Events","P(X)","Prior Prob","P(X)","Conditional Prob","P(X)","Joint Prob","P(X)","Prior Probability"]
["Graduate","P(A1)",0.47,"P(M | A1)",{"$f":"1-E3","v":0.5},"P(A1 AND M)",{"$f":"E10*C10","v":0.23499999999999999},"P(A1 | M)",{"$f":"G10/$G$12","v":0.44634377967711303}]
["Not Graduate","P(A2)",{"$f":"1-C10","v":0.53},"P(M | A2)",0.55000000000000004,"P(A2 AND M)",0.29150000000000004,"P(A2 | M)",{"$f":"G11/$G$12","v":0.55365622032288708}]
[null,null,null,null,"Total","P(M)",{"$f":"SUM(G10:G11)","v":0.52649999999999997},null,{"$f":"SUM(I10:I11)","v":1}]
[]
[]
[null,null,null,null,"d",{"$f":"F5","v":"P(W)"},{"$f":"G5","v":0.47350000000000003}]
[null,null,null,null,null,{"$f":"F12","v":"P(M)"},{"$f":"G12","v":0.52649999999999997}]
[null,null,null,null,null,null,{"$f":"SUM(G15:G16)","v":1}]

{"sheet":"(52-53)","index":33,"n_rows":32,"n_cols":7,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
[null,null,null,"Applied To More Than One School"]
[null,null,null,"Yes","No","Total"]
[null,"Age Group","< =23",207,201,{"$f":"SUM(D3:E3)","v":408}]
[null,null,"24-26",299,379,678]
[null,null,"27-30",185,268,453]
[null,null,"31-35",66,193,259]
[null,null,">=36",51,169,220]
[null,null,"Total",{"$f":"SUM(D3:D7)","v":808},{"$f":"SUM(E3:E7)","v":1210},2018]
[]
[null,null,null,"Applied To More Than One School"]
[null,null,null,"Yes","No","Total"]
["a","Age Group","< =23",{"$f":"D3/$F$8","v":0.10257680872150644},9.9603567888999003E-2,0.20218037661050545]
[null,null,"24-26",0.14816650148662042,0.18780971258671952,0.33597621407333994]
[null,null,"27-30",9.1674925668979182E-2,0.13280475718533202,0.22447968285431119]
[null,null,"31-35",3.2705649157581763E-2,9.5639246778989093E-2,0.12834489593657086]
[null,null,">=36",2.5272547076313181E-2,8.374628344895936E-2,0.10901883052527254]
[null,null,"Total",0.40039643211100101,0.59960356788899905,1]
[]
["b","P(<23 years)",{"$f":"F12","v":0.20218037661050545}]
["c","P(<26 years)",{"$f":"SUM(F14:F16)","v":0.46184340931615459}]
["d","P(Applied more than 1 school)",{"$f":"D17","v":0.40039643211100101}]
[]
["53a","P(24-26 | Applied more than 1 school)",{"$f":"D13/D17","v":0.37004950495049505},{"$f":"TEXT(D13,\"0.00%\")&\"/\"&TEXT(D17,\"0.00%\")&\" or \"&D4&\"/\"&D8","v":"14.82%/40.04% or 299/808"},null,null,{"$f":"D4/D8","v":0.37004950495049505}]
["53b","P(Applied more than 1 school | >36)",{"$f":"D16/F16","v":0.23181818181818181},{"$f":"TEXT(D16,\"0.00%\")&\"/\"&TEXT(F16,\"0.00%\")&\" or \"&D7&\"/\"&F7","v":"2.53%/10.90% or 51/220"},null,null,{"$f":"D7/F7","v":0.23181818181818181}]
["53c","P(24-26 OR Applied to more than 1 school)",{"$f":"F13+D17-D13","v":0.58820614469772048},{"$f":"TEXT(F13,\"0.00%\")&\"+\"&TEXT(D17,\"0.00%\")&\"-\"&TEXT(D13,\"0.00%\")","v":"33.60%+40.04%-14.82%"}]
["53d","P(>=31 | Only 1 school)",{"$f":"SUM(E15:E16)/E17","v":0.29917355371900822},{"$f":"\"(\"&TEXT(E15,\"0.00%\")&\"+\"&TEXT(E16,\"0.00%\")&\")/\"&TEXT(E17,\"0.00%\")","v":"(9.56%+8.37%)/59.96%"}]
["53e","No because the Marginal Probabilities do not equal the Conditional Probabilities"]
[null,"Example:"]
[null,"P(24-26 | Applied more than 1 school)",{"$f":"C23","v":0.37004950495049505}]
[null,"P(24-26)",{"$f":"F13","v":0.33597621407333994}]
[null,"Because P(A) <> P(A | B)"]
[null," ** <> means not"]

{"sheet":"58","index":34,"n_rows":39,"n_cols":6,"rows_kept":39,"cut":false,"hidden":false,"merged":[]}
[null,"Events"]
[null,"Blogger","B"]
[null,"Non Blogger","NB"]
[null,"Young (18-29) Adult","YA"]
[null,"Older (30 or older) Adult","OA"]
[]
[null,"Probabilities Given"]
[null,"P(Adults are Bloggers)",0.08,"P(B)"]
[null,"P(Adults are NOT Bloggers)",{"$f":"1-C8","v":0.92},"P(NB)"]
[null,"P(Young Adults | Bloggers)",0.54,"P(YA | B)"]
[null,"P(Young Adults | Non Bloggers)",0.24,"P(YA | NB)"]
[null,null,{"$f":"C10*C8","v":4.3200000000000002E-2},"P(YA AND B) = P(YA | B) * P(B)"]
[null,null,{"$f":"C9*C11","v":0.2208},"P(YA AND NB) = P(YA | NB) * P(NB)"]
[]
[null,"Young Adults","Older Adults","Totals"]
["Blogger",{"$f":"C12","v":4.3200000000000002E-2},{"$f":"D16-B16","v":3.6799999999999958E-2},{"$f":"D18-D17","v":7.999999999999996E-2}]
["Non Blogger",{"$f":"C13","v":0.2208},{"$f":"D17-B17","v":0.69920000000000004},{"$f":"C9","v":0.92}]
["Totals",{"$f":"SUM(B16:B17)","v":0.26400000000000001},{"$f":"D18-B18","v":0.73599999999999999},1]
[]
[null,"Young Adults","Older Adults","Totals"]
["Blogger",{"$f":"B16*10000","v":432},367.9999999999996,799.99999999999955]
["Non Blogger",2208,6992,9200]
["Totals",2640,7360,10000]
[]
[]
[null,"Young Adults","Older Adults","Totals"]
["Blogger",{"$f":"B21/$D$23","v":4.3200000000000002E-2},3.6799999999999958E-2,7.999999999999996E-2,null,"Joint"]
["Non Blogger",0.2208,0.69920000000000004,0.92]
["Totals",0.26400000000000001,0.73599999999999999,1]
[]
[null,"Young Adults","Older Adults","Totals"]
["Blogger",{"$f":"B21/B$23","v":0.16363636363636364},4.9999999999999947E-2,7.999999999999996E-2,null,"Conditional"]
["Non Blogger",0.83636363636363631,0.95,0.92]
["Totals",1,1,1]
[]
[null,"Young Adults","Older Adults","Totals"]
["Blogger",{"$f":"B21/$D21","v":0.54000000000000026},0.45999999999999974,1,null,"Conditional"]
["Non Blogger",0.24,0.76,1]
["Totals",0.26400000000000001,0.73599999999999999,1]