For married couples living in Springfield MA, the probability that the husband w

Question

For married couples living in Springfield MA, the probability that the husband will vote on a bond referendum is 0.21, the probability that his wife will vote in the referendum is 0.28, and the probability that both husband and wife will vote is 0.15. What is the probability that: a) At least one member of a married couple will vote? (Husband, wife or both) b) A wife will vote, given that her husband will vote? c) A husband will vote, given that his wife will not vote? d) Can we assume that the decision of the wife to vote is independent of her husband decisions and why? Let X denotes the reaction time, in seconds; to a certain stimulants and Y denote the temperature at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density. f(x, y) = {4xy, 0

Explanation / Answer

Q.1 Pr (Husband) = P(H) = 0.21

Pr(Wife) = P(W) = 0.28 and

Pr ( Both Husband and wife will vote) = P( H U W) = 0.15

(a) At leat one member will vote = P(H) + P(W) - P( H U W) = 0.21 + 0.28 - 0.15 = 0.34

(b) A wife will vote, given that her husband will vote?

= P(W l H ) = 0.15/0.21 = 0.7143

(c) A husband will vote, given that his wife will vote?

= P ( H l W) = 0.15/ 0.28 = 0.536

(d) Here we have to know that the events W and H are independent of each other.so for that to be true

P( H U W) = P(H) *P(W)

P(H) *P(W) = 0.21 * 0.28 = 0.0588 0.15 = P( H U W)

so These two events are not independent of each other.

so

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