Answer in Statistics and Probability for Shema Derrick #205145

In a certain federal prison, it is known that 2/3 of the inmates are under 25 years of age. It is also known that 3/5 of the inmates are male and that 5/8 of the inmates are female or 25 years of age or older. What is the probability that a prisoner selected at random from this prison is female and at least 25 years old?

Let “A” denotes the event “inmate is under 25 years of age”.

Let “M” denotes the event “inmate is a male”.

Let “F” denotes the event “inmate is a female”.

Given “P(A)=dfrac{2}{3}, P(M)=dfrac{3}{5}, P(Fcup A’)=dfrac{5}{8}.”

“P(A’)=1-P(A)=1-dfrac{2}{3}=dfrac{1}{3}”

“P(F)=1-P(M)=1-dfrac{3}{5}=dfrac{2}{5}”

“P(Fcap A’)=P(F)+P(A’)-P(Fcup A’)”

“P(Fcap A’)=dfrac{2}{5}+dfrac{1}{3}-dfrac{5}{8}=dfrac{48+40-75}{120}”

“=dfrac{13}{120}”