Question

For married couples living in a certain suburb, the probability that the husband will vote on a bond
referendum is 0.25, the probability that the wife will vote on the referendum is 0.20. The probability
that a husband will vote on the bond referendum, given that his wife will vote, is 0.75. What is the
probability that
a. both husband and wife will vote?
b. a wife will vote, given that her husband will vote?
c. at least one member of a married couple will vote?

Answer 1

P(husband will vote) = 0.25

P(wife will vote) = 0.2

P(husband will vote | wife will vote) = 0.75

a) P(both husband and wife will vote) = P(husband will vote | wife will vote) * P(wife will vote) = 0.75 * 0.2 = 0.15

b) P(wife will vote | husband will vote) = P(both husband and wife will vote) / P(husband will vote) = 0.15 / 0.25 = 0.6

c) P(at least one member will vote) = P(husband will vote) + P(wife will vote) - P(both husband and wife will vote) = 0.25 + 0.2 - 0.15 = 0.3