Question

A committee of two persons is selected from two men and two women. The probability that the committee will have exactly one woman is

• A. $\frac{1}{6}$
• B. $\frac{2}{3}$
• C. $\frac{1}{3}$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$\frac{2}{3}$

Probability of exactly one woman being selected $=\frac{\text{Permutation of exactly one woman and one man being selected}}{\text{Permutation of any 2 people being selected}}=\frac{{}^2{C}_1{\times }^2{C}_1}{{}^4{C}_2}=\frac{4}{6}=\frac{2}{3}$