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 selected person is female, is

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

Answer 1

Answer: (B)

$\frac{1}{2}$

This is a question of conditional probability, the condition being given here that the selected person is a female.

Since the selected person is a female, the sample space becomes $6$ since there were $6$ females in total.

Next, out of those $6$ only $3$ females are above $40$ years of age and so the probability that the selected female is aged above $40$ becomes $\frac{3}{6}=\frac{1}{2}$