Question

In a management trainee program, 80% female and 20% male. 90% of the females went to college. 78% of the males went to college. A management trainee is selected at random. What is the probability that the person selected is a female who did NOT go to college?

Answer 1

Question #15160In a management trainee program,0. 80 female and 0.20 male.0. 90 of the females went to college. 0.78 of the males went to college. A management trainee is selected at random. What is the probability that the person selected is a female who did NOT go to college? .

Solution. Denote by $F$ the event that selected at random person is female, and the same thing for $M$. The condition implies that $\mathsf{P}(F)=1-\mathsf{P}(M)=0.8$.Denote by $A$ the event that person selected at random did not go to the college, hence $\mathsf{P}(A|F)=0.1$ and $\mathsf{P}(A|M)=0.12$ We are interested in the probability $\mathsf{P}(F\cap A)=\mathsf{P}(A|F)\mathsf{P}(F)=0.1\cdot 0.8=0.08$.

Answer 0.08.