Question

In a survey in a certain year of married couples with earnings, 93% of all husbands were employed. Of all employed husbands, 73% of their wives were also employed. Noting that either the husband or wife in a couple with earnings had to be employed, find the probability that the husband of an employed woman was also employed. (Round your answer to four decimal places.)

Answer 1

P(employed husband) = 0.93

P(employed wife | employed husband) = 0.73

P(employed husband and wife) = 0.93 x 0.73 = 0.6789

P(husband or wife employed) = 1

P(only wife is employed) = 1 - 0.93 = 0.07

P(wife is employed) = 0.07 + 0.6789 = 0.7489

Probability that the husband of an employed woman was also employed, P(employed husband | employed wife) = P(employed husband and wife) / P(employed wife)

= 0.6789/0.7489

= 0.9065