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

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

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) = (P(Z'') * P(M|Z''))/(P(M))`

`P(Z''| M) =  (0.4 * 0.61)/(0.502)`

`P(Z''| M) = 0.4860`