{"text_format":"3","workbook":"xls","n_sheets":2,"sheets":["Question 37","Question 5"],"not_rendered":{"charts":1,"external_links":2,"comments":1},"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"Question 37","index":0,"n_rows":31,"n_cols":5,"rows_kept":31,"flags":["formulas_cached_only"]}
[]
[]
[null,"number successes",7,7,7]
[null,"number trials",10,10,10]
[null,"probability",{"v":0.45,"d":"45%"},{"v":0.5,"d":"50%"},{"v":0.55,"d":"55%"}]
[null,"cumulative True or False",0,0,0]
[null,"Binomial Prob",{"v":0.07460310631640622,"d":"7.46%"},{"v":0.11718750000000006,"d":"11.72%"},{"v":0.16647829287890628,"d":"16.65%"}]
[null,"lower bound - 1",5,5,5]
[null,"upper bound",10,10,10]
[null,"Prob of falling between the bounds, > min =max",{"v":0.26156270075449206,"d":"26.2%"},{"v":0.3769531250000001,"d":"37.7%"},{"v":0.5044045916529296,"d":"50.44%"}]
[]
[]
[]
[]
[null,"Coin","Pr{heads}","Pr{ 7 | coin}","Pr{coin | 7}"]
[null,"Gold",{"v":0.55,"d":"55.0%"},{"v":0.16647829287890628,"d":"16.65%"},{"v":0.46467414071615964,"d":"46.5%"}]
[null,"Silver",{"v":0.5,"d":"50.0%"},{"v":0.11718750000000006,"d":"11.72%"},{"v":0.32709370046690694,"d":"32.7%"}]
[null,"Bronze",{"v":0.45,"d":"45.0%"},{"v":0.07460310631640622,"d":"7.46%"},{"v":0.20823215881693338,"d":"20.8%"}]
[null,null,"average =",{"v":0.11942296639843752,"d":"11.94%"},{"v":1,"d":"100.0%"}]
[]
[null,"Observe someone who tossed 7 heads"]
[null,"Prob that they have a gold coin?"]
[null,"Prob{gold | 7} = Prob{7 | gold}*Prob{gold} / Prob{7}"]
[null,"Under second set of probs, Prob{gold | 10} =",{"v":0.46467414071615964,"d":"46.5%"}]
[]
[]
[null,"Coin","Pr{heads}","Pr{7,8,9,10}","Pr{6,7,8,9,10}"]
[null,"Gold",{"v":0.55,"d":"55.0%"},{"v":0.2660379450308593,"d":"26.60%"},{"v":0.5044045916529296,"d":"50.44%"}]
[null,"Silver",{"v":0.5,"d":"50.0%"},{"v":0.171875,"d":"17.19%"},{"v":0.376953125,"d":"37.70%"}]
[null,"Bronze",{"v":0.45,"d":"45.0%"},{"v":0.10199494557773425,"d":"10.20%"},{"v":0.26156270075449206,"d":"26.16%"}]
[null,"Prob of future performance",null,{"v":0.20107881097892433,"d":"20.11%"},{"v":0.45059876935943216,"d":"45.06%"}]

{"sheet":"Question 5","index":1,"n_rows":16,"n_cols":8,"rows_kept":16,"flags":["formulas_cached_only"]}
[]
[null,12,"trials"]
[null,8,"black"]
[null,4,"red"]
[null,0.7,"= probability of drawing black in bag with 300 reds"]
[null,0.3,"= probability of drawing black in bag with 700 reds"]
[null,{"v":0.45,"d":"45%"},"bags contain predominantly black chips (300 reds)"]
[null,{"v":0.55,"d":"55%"},"bags contain predominantly red chips (700 reds)"]
[null,"Prob{8 blacks |p=.7} =",null,{"v":0.23113969609499999,"d":"23.11%"}]
[null,"Prob{8 blacks |p=.3} =",null,{"v":0.00779771569499999,"d":"0.78%"}]
[]
[null,"Prob{8 blacks in 12 trials} = ",null,{"v":0.108301606875,"d":"10.8%"}]
[]
[null,"Let p = the proportion of black chips in the bag."]
[null,"Bayes rule implies"]
[null,"Prob{p=.7|8 blacks} = Prob{8 blacks |p = .7}*Prob{p = .7}/Prob{8 blacks}  =",{"$nulls":5},{"v":0.9604,"d":"96.04%"}]