Question

Out of 13 applications for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman is

• A. $\frac{5}{13}$
• B. $\frac{14}{39}$
• C. $\frac{25}{39}$
• D. $\frac{10}{13}$

Answer 1

Answer: (C)

$\frac{25}{39}$

Answer 2

Total ways to select 2 persons from 13:
$\binom{13}{2} = 78$

Ways to select 2 men (no women):
$\binom{8}{2} = 28$
Probability of no women:
P(\text{no women}) = \frac{28}{78} \\\= \frac{14}{39}

Probability of at least one woman:
P(\text{at least one woman}) = 1 - \frac{14}{39} \\\= \frac{25}{39}

The probability that at least one of the selected persons will be a woman is $\frac{25}{39}$.