Question

In a group 14 males and 6 females, 8 and 3 of the males and females respectively are aged above 40 years. The probability that a person selected at random from the group is aged above 40 years, given that the slelected person is a female, is

• A. $\frac{2}{7}$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $\frac{5}{6}$

Answer 1

The correct option is B $\frac{1}{2}$

Let $A$ is the event in which selected person is female and $B$ is the event in which the selected person is above 40 years.
Apply the conditional probability method
$P\left(\frac{B}{A}\right)=\frac{P(B\cap A)}{P\left(A\right)}$
$=\frac{\frac{3}{20}}{\frac{6}{20}}$
$=\frac{1}{2}$