A recent study shows that unemployment does not impact males and females in the same way (Newsweek, April 20, 2009). According to a Bureau of Labor Statistics report, 8.5% of those who are eligible to work are unemployed. The unemployment rate is 8.8% for eligible men and only 7.0% for eligible women. Suppose 52% of the eligible workforce in the U. S. consists of men. a. You have just heard that another worker in a large firm has been laid off. What is the probability that this worker is a man?b. You have just heard that another worker in a large firm has been laid off. What is the probability that this worker is a woman?

(a) The probability that a worker who is unemployed is a man is 0.5384.

(b) The probability that a worker who is unemployed is a woman is 0.3953.

Explanation:

Let's denote the events as follows:

U = An eligible person is unemployed

M = An eligible person is a man

W = An eligible person is a woman

Given:

P (U) = 0.085, O (U | M) = 0.088, P (U | W) = 0.070 and P (M) = 0.52.

The probability that an eligible person is a woman is,

P (W) = 1 - P (M) = 1 - 0.52 = 0.48

(a)

It is provided that a worker is unemployed.

Determine the probability that the worker is a man as follows:

Thus, the probability that a worker who is unemployed is a man is 0.5384.

(b)

It is provided that a worker is unemployed.

Determine the probability that the worker is a woman as follows:

Thus, the probability that a worker who is unemployed is a woman is 0.3953.

answer; vertical marketing system;

the answer is a. $209,000