Question

According to a recent report, 60% of U.S. college graduates cannot find a full time job in their chosen profession. Assume 57% of the college graduates who cannot find a job are female and that 39% of the college graduates who can find a job are female. Given a male college graduate, find the probability he can find a full time job in his chosen profession?

Answer 1

Answer:

The value is $P(Z''| M) = 0.4860$

Step-by-step explanation:

From the question we are told that

The proportion that can not find a full time job in their chosen profession is

$P(Z) = 0.60$

The proportion that can not find a full time job in their chosen profession who are female is $P(F|Z) = 0.57$

The proportion that can find a full time job in their chosen profession who are female is $P(F|Z'') = 0.39$

The proportion that cannot find a full time job in their chosen profession who are male is $P(M|Z) = 1 - 0.57 = 0.43$

The proportion that can find a full time job in their chosen profession who are male is $P(M|Z'') = 1- 0.39 = 0.61$

The proportion that can find a full time job in their chosen profession is

$P(Z'') = 1- 0.60 = 0.4$

Generally the probability that the college graduates is a male is mathematically evaluated using Bayes' Rule as follows

$P(M) = P(Z ) * P(MI Z) + P(Z'') * P(M|Z'')$

$P(M) = 0.6 * 0.43 + 0.4 * 0.61$

$P(M) = 0.502$

Generally the probability he can find a full time job in his chosen profession is mathematically evaluated using Bayes' Rule as follows

$P(Z''| M) = \frac{P(Z'') * P(M|Z'')}{P(M)}$

              $P(Z''| M) = \frac{0.4 * 0.61}{0.502}$

             $P(Z''| M) = 0.4860$