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 NOT attend college?

In this case, we want to know the probability of two events happening , the first even is that the person selected is woman. We have this probability , it is 80% ( 0.80)

The other even is NOT attended college. We know the percentage of the women who attended, the other option is Not attended ( the complement). The Complement Rule states that the sum of the probabilities of an event and its complement must equal 1.

So, the probability of a women not attended college is = 1-0.90=0.10

We are looking the probability of 2 event that occur at the same time, so we have to multiply the probability of both events.

Probability that the person selected is a female who did NOT attend college= Probability that the person selected is a female * Probability that the person selected not attended college

Probability= 0.80 * 0.10=0.08