Question

in a survey in a certain year of straight married couples with earnings, 91% of all husbands were employed. of all employed husbands, 71% 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 two decimal places.)

Answer 1

The probability that the husband of an employed woman is also employed is 0.91, or 91%

The Breakdown

Using conditional probability.

A: Husband is employed

B: Wife is employed

We are given:

P(A) = 0.91 (probability that a husband is employed)

P(B|A) = 0.71 (probability that a wife is employed given that the husband is employed)

We need to find P(A|B), which is the probability that the husband is employed given that the wife is employed.

Using Bayes' theorem, we have:

P(A|B) = (P(B|A) × P(A)) / P(B)

To calculate P(B), we can use the law of total probability:

P(B) = P(B|A) × P(A) + P(B|A') × P(A')

Where A' represents the complement of event A (husband is not employed).

Given that either the husband or wife in a couple with earnings had to be employed, we can assume that P(A') = 0.

Plugging in the values, we get:

P(B) = P(B|A) × P(A) + P(B|A') × P(A')

= P(B|A) × P(A)

P(A|B) = (P(B|A) × P(A)) / P(B)

= (0.71 × 0.91) / (0.71 × 0.91)

= 0.91

Therefore, the probability that the husband of an employed woman is also employed is 0.91, or 91% (rounded to two decimal places).