Question

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. Based on this information, the probability that the person selected is a female who did NOT attend college is?

Answer 1

Answer: 0.08

Explanation:

Given : The probability that the person is female : P(F)=80%=0.080

The probability that the females attended college : P(A|F)=90%=0.90

Then, the probability that the females do not attended college :

`P(A^c|F)=1-P(A|F)=1-0.90=0.10`

Now using conditional probability formula :

`P(M|N)=(P(M\cap N))/(P(N))`

We get,

`P(A^c|F)=(P(A^c\cap F))/(P(F))`

Substitute the values , we get

`0.10=(P(A^c\cap F))/(0.80)\\\\\Rightarrow\ P(A^c\cap F)=0.80*0.10=0.08`

Hence, the probability that the person selected is a female who did NOT attend college is 0.08 .