Record of a company show that 15% of the employees have only a high school diplo

Question

Record of a company show that 15% of the employees have only a high school diploma (H), 75% have and 10% have graduate degrees Of those with only a high school diploma, 12% hold management positions, whereas, of these having bachelor digress, 58% hold management positions. Finally, 82% of the employees who have graduate degrees hold management positions. What percentage of employees holds management positions? 53.5% Given that a person holds a management position, what is the probability that she/he has a graduate degree? 0.1533

Explanation / Answer

Let M shows the event that person holds a management degree. Here we have

P(H) = 0.15, P(B) = 0.75, P(G) = 0.10,

P(M|H) = 0.12, P(M|B) = 0.58, P(M|G) = 0.82

(a)

By the law of total probability, we have

P(M) = P(M|H)P(H) +P(M|B)P(B)+P(M|G)P(G) = 0.12*0.15+0.58*0.75+0.82*0.10=0.535

(b)

By the Baye's theorem we have

P(G|M) = [P(M|G)P(G) ] / P(M) = [ 0.82*0.10] / 0.535 = 0.1533

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