In a management trainee program,80% of the trainees are female,while 20% are male. Ninety percent of the females attended college; 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 attended 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. Using the conditional probability formula, we have:

P(female and attended college) = P(attended college | female) * P(female)

From the given information, P(female) = 0.8 and P(attended college | female) = 0.9. Therefore,

P(female and attended college) = 0.9 * 0.8 = 0.72

So, the probability of selecting a female who attended college is 0.72, which is given by the expression P(female)P(attended college | female). Therefore, the correct choice is C. The other choices are incorrect because they do not take into account both the probability of being a female and the probability of attending college, or they use conditional probability incorrectly.

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