Question

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 6/8 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?

Answer 1

Let A be the event which denotes that the inmates are under 25 years of age.

A^C denotes that the inmates are at least 25 years of age.

$P(A) = \frac{2}{3} \\ P(A^C) = 1 -P(A) \\ = 1 -\frac{2}{3} \\ = \frac{1}{3}$

Let M be the event which denotes that the inmate is male.

M^C denotes that a inmate is female

$P(M) = \frac{3}{5} \\ P(M^C) = 1 -P(M) \\ = 1 -\frac{3}{5} \\ = \frac{2}{5}$

Now, we have to find the probability that a prisoner selected at random from the prison is female at least 25 years old

$P = \frac{1}{3} \times \frac{2}{5} \\ = \frac{2}{15} \\ = 0.1333$

Answer: 0.1333