You are working for a renowned head hunting company midtown

You are working for a renowned head hunting company midtown Manhattan. Your job is to identify high potentials for the financial services industry. The prior probability that someone you will consider is a high potential is 0.03. If someone is a high potential, their probability of having a degree from an Ivy League school is 0.6 and the probability that they have an Ivy League degree if they are not a high potential is 0.05. The person you are considering has an Ivy League degree. What is the probability that they are a high potential? A. 0.03 B. 0.27 C. 0.33 D. 0 E. 0.66

Solution

Let

H = high potential
D = has degree

Thus,

P(H|D) = P(H) P(D|H) / P(D)

As

P(D) = P(H) P(D|H) + P(H\') P(D|H\') = (0.03)*(0.6) + (1-0.03)*(0.05) = 0.0665

Thus,

P(H|D) = P(H) P(D|H) / P(D) = 0.03*0.6/0.0665 = 0.270676692 = 0.27 [ANSWER, OPTION B]