Bayes\' Theorem You are given two sets of raffle tickets, both of which contain

ID: 3320455 • Letter: B

Question

Bayes' Theorem You are given two sets of raffle tickets, both of which contain winners. You can select 4 tickets from either one pile or the other, but not both. Your initial chan 20%. Your chance of having selected a ticket chance of having selected a ticket from set 1 given that it is a winner is 35%. Likewise, your chance of having selected a ticket from set 1 given that it is not a winner 60%. Determine the probability of having a winning ticket given that you have selected all four tickets from set 1. from set 2 given that it is a winner is 40% and your

Explanation / Answer

By Bayes theorem we know that

P(A given B) or P(A | B) = P(A B)/P(B)

Given that

i)P(getting a winning ticket) or P( slected a winning ticket) = 0.2 or 20%

ii) P(selected a ticket from set 2 given that it is a winner) = 0.35 or 35%

P(selected from set 2 | slected a winning ticket) = 0.35

P(selected from set 2 and slected a winning ticket)/P( slected a winning ticket) = 0.35

P(selected from set 2 and slected a winning ticket) = 0.35*P( slected a winning ticket) = 0.35*0.2 = 0.07

we alseo know that P( slected a winning ticket) = P(selected from set 1 and slected a winning ticket)+ P(selected from set 2 and slected a winning ticket)

so P(selected from set 1 and slected a winning ticket) = 0.2-0.07 = 0.13

iii)P(selected a ticket from set 1 given that it is not a winner) = 0.6 or 60%

P(selected from set 1 and slected a non winning ticket)/P( slected a winning ticket) = 0.60

P(selected from set 1 and slected a non winning ticket) = 0.60*P( slected a non winning ticket) = 0.60*(1-0.2) = 0.48

P(selected from set 1) = P(selected from set 1 and slected a winning ticket) +P(selected from set 1 and slected a non winning ticket) = 0.13+0.48 = 0.61

By Bayes theorem

probability of having a winning ticket given that you have selected all four tickets from set 1 =

P(selected from set 1 and slected a winning ticket)/P(selected from set 1)

= 0.13/0.61 = 0.2131

so probability of having a winning ticket given that you have selected all four tickets from set 1 is 0.2131

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Bayes\' Theorem You are given two sets of raffle tickets, both of which contain

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