In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 78% 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 attended college, which can be expressed as P(female and did attend college) or P(did attend college | female). Using the formula for conditional probability, we have:

P(did attend college | female) = P(female and did attend college) / P(female)

We already know that P(female) = 0.8 and P(female and did attend college) = 0.8 x 0.9 = 0.72. Substituting these values, we get:

P(did attend college | female) = 0.72 / 0.8 = 0.9

Therefore, the probability that the selected person is a female who did attend college is 0.9 or 90%.

In a Management Trainee Program, 80% of the Trainees Are