1. For a married couple living in a certain city, the probability that the husba
ID: 3321033 • Letter: 1
Question
1. For a married couple living in a certain city, the probability that the husband will vote in a school board election is 0.5, the probability the wife will vote is 0.6, and the probability that both will vote is 0.4. (a) Given that husband will vote in certain school board election, find the probability that wife will also vote in the school board election. (5 points) (b) Given that at least one person of a particular couple living in the city will vote, find the conditional probability that wife will vote in the school board election. (5 points)Explanation / Answer
P(husband) = 0.5 P(wife) = 0.6 P(both) = 0.4.
(a) We have by Baye's theorem
P(wife|husband)
= P(both) / P(husband)
= 0.4 / 0.5
= 0.8.
(b) P(atleast one) = P(husband) + P(wife) - P(both)
= 0.5 + 0.6 - 0.4 = 0.7.
=> P(wife|atleast one) = P(wife and atleast one) / P(atleast one)
= P(wife) / P(atleast one)
= 0.6 / 0.7
= 0.8571.
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