Question

A bag contains twelve pairs of socks and four socks are picked up at random. The probability that there is a least one pair is equal to

• A. $\frac{20}{161}$
• B. $\frac{22}{161}$
• C. $\frac{120}{161}$
• D. $\frac{11}{161}$

Answer 1

The correct option is D $\frac{11}{161}$

Probability of getting no pair $=\frac{24}{24}\times \frac{22}{23}\times \frac{20}{22}\times \frac{18}{20}=\frac{120}{161}$
Therefore probability of getting at least one pair $=1-\frac{120}{161}=\frac{41}{161}.$