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Probability Problem Set 2

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Probability Problem Set 2

by theachiever » Thu Nov 01, 2012 1:27 am
A polling company reports that there is a 40% chance that a certain candidate will win the next election.If the candidate wins,there is a 60% chance that she will sign Bill X and no other bills.
If she decides not to sign Bil X,she will sign either Bill Y or Bill Z,chosen randomly.What is the chance that the candidate will sign Bill Z?
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by pemdas » Thu Nov 01, 2012 3:17 am
theachiever wrote:A polling company reports that there is a 40% chance that a certain candidate will win the next election.If the candidate wins,there is a 60% chance that she will sign Bill X and no other bills.
If she decides not to sign Bil X,she will sign either Bill Y or Bill Z,chosen randomly.What is the chance that the candidate will sign Bill Z?
According to condition a candidate will win but refuse to sign Bill X, that is 40% chance of candidate's win combined with (100-60)% chance of not signing Bill X, i.e. singing either Bill Y or Z.

0,4*(1-0,6)=p(Bill Y) + p(Bill Z). Since we consider randomness in selection of Bills Y or Z, that is no special preference between two Bills and either one can be selected, there is 50/50 % chance each will be selected. Hence p(Bill Z)=p(Bill Y) Or 0,4*0,4=p(Bill Z) + p(Bill Z), 0,16=2*p(Bill Z) and p(Bill Z)=0,16/2=0,08

chance that the candidate will sign Bill Z is 0,08 or 8%
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