In a survey in a certain year of married couples with earnings, 99% of all husbands were employed. Of all employed husbands, 77% 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.)

Accepted Solution

Answer: Our required probability is 0.7778.Step-by-step explanation:Since we have given that Probability that husbands were employed P(H) = 99%Probability that off all husbands, wives were also employed P(H∩W) = 77%We will use "conditional probability" to find the husband of an employed women was also employed.Probability that the husband of an employed woman was also employed is given by[tex]P(W|H)=\dfrac{P(H\cap W)}{P(H)}=\dfrac{0.77}{0.99}=0.7778[/tex]Hence, our required probability is 0.7778.