In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did attend college?
A) P (female) P(did not attend college | female)
B) P (did attend college) P (female | did not attend college)
C) P (female) P(did attend college | female)
D) P (did attend college)

Question

Quizplus · Accepted Answer

We want to find the probability of selecting a female who did attend college. Using Bayes' theorem, we can write:
P(female and did attend college) = P(female) * P(did attend college | female)
We are given that 80% of the trainees are female, so P(female) = 0.8. We are also given that 90% of the females attended college, so P(did attend college | female) = 0.9. Therefore,
P(female and did attend college) = 0.8 * 0.9 = 0.72
Thus, the probability of selecting a female who did attend college is 0.72.

In a Management Trainee Program, 80 Percent of the Trainees