Question

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?

Answer 1

Answer: 0.72

Explanation:

Let A be the event that denotes that trainees are females and B denotes the event that the trainees attended college.

Given : The probability that the trainees are female : P(A) = 0.8

The probability that females attended college : P(B|A) =0.90 [Conditional probability]

Now, the probability that the person selected is a female who attended college is given by :-

`P(A\cap B)=P(B|A)* P(A)\\\\\Rightarrow\ P(A\cap B)=0.90*0.80=0.72`

Hence, the probability that the person selected is a female who attended college = 0.72