In a management trainee program, 80 percent of the trainees are female, 20 percent male. 90 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?
It doesn't matter how many trainees there are, so let's suppose there are $100$. Then $80$ are female, and $72$ of the $80$ went to college, so the probability the person selected is a female who attended college is ... ?
The probability of two independent events is $P(AB) = P(A)P(B)$. In this situation, P(A), where A is that the selected person is female is $.8$, and P(B), where B is that a given female went to college is $.9$, so the final answer is $$ P(AB) = P(A)P(B) = (.8)(.9) = .72 $$