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

The Correct Option is C

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 \(\frac{25}{39}\).