Answer in Statistics and Probability for Shema Derrick #205147

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

U- under 25

M- male

F-female

“P(U)=frac{2}{3}”

“P(M)=frac{3}{5}”

“P(Fcupoverline U)=frac{5}{8}”

“P(Fcapoverline U)”

Let

“P(Mcapoverline U)=x”

Then

“P(Mcap{U})=P(M)-P(Mcap overline U)=frac{3}{5}-x”

Similarly

“P(Fcap U)=P(U)-P(Mcap U)=frac{2}{3}-frac{3}{5}+x=frac{1}{15}+x”

“P(Fcapoverline U)= P(F)-P(Fcap U)”

“=frac{5}{8}-x-(frac{1}{15}-x-)=frac{67}{120}-2x”

Now

“P(M)+P(F)=1”

“frac{3}{5}+frac{5}{8}-x=1”

Solving for x, we have,

“x=frac{9}{40}”

Thus,

“P(Fcapoverline U)=frac{67}{120}-2(frac{9}{40})=frac{13}{120}”