For a married couple living in a certain city, the probability that the husband

Question

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 1. 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. (S points)

Explanation / Answer

P( husband ) = 0.5,
P( wife ) = 0.6,
P( both ) = 0.4

a) Using bayes theorem, we get here:

P( Wife | husband ) = P( both ) / P( husband ) = 0.4 / 0.5 = 0.8

Therefore 0.8 is the required probability here.

b) Using law of addition of probability, we get:

P( husband or wife ) = P( husband ) +P( wife ) - P( both ) = 0.5 + 0.6 - 0.4 = 0.7

Now using bayes theorem, we get:

P( wife | husband or wife ) = P( wife ) / P( husband or wife ) = 0.6 / 0.7 = 0.8571

Therefore 0.8571 is the required probability here.

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