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

Step-by-step 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 :

$P(M|N)=\dfrac{P(M\cap N)}{P(N)}$

We get,

$P(A^c|F)=\dfrac{P(A^c\cap F)}{P(F)}$

Substitute the values , we get

$0.10=\dfrac{P(A^c\cap F)}{0.80}\\\\\Rightarrow\ P(A^c\cap F)=0.80\times0.10=0.08$

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