Answer:
The value is [tex]P(Z''| M) = 0.4860[/tex]
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
[tex]P(Z) = 0.60[/tex]
The proportion that can not find a full time job in their chosen profession who are female is [tex]P(F|Z) = 0.57[/tex]
The proportion that can find a full time job in their chosen profession who are female is [tex]P(F|Z'') = 0.39[/tex]
The proportion that cannot find a full time job in their chosen profession who are male is [tex]P(M|Z) = 1 - 0.57 = 0.43[/tex]
The proportion that can find a full time job in their chosen profession who are male is [tex]P(M|Z'') = 1- 0.39 = 0.61[/tex]
The proportion that can find a full time job in their chosen profession is
[tex]P(Z'') = 1- 0.60 = 0.4[/tex]
Generally the probability that the college graduates is a male is mathematically evaluated using Bayes' Rule as follows
[tex]P(M) = P(Z ) * P(MI Z) + P(Z'') * P(M|Z'')[/tex]
[tex]P(M) = 0.6 * 0.43 + 0.4 * 0.61[/tex]
[tex]P(M) = 0.502 [/tex]
Generally the probability he can find a full time job in his chosen profession is mathematically evaluated using Bayes' Rule as follows
[tex]P(Z''| M) = \frac{P(Z'') * P(M|Z'')}{P(M)}[/tex]
[tex]P(Z''| M) = \frac{0.4 * 0.61}{0.502}[/tex]
[tex]P(Z''| M) = 0.4860[/tex]
