Question

A man has $3$ pairs of black socks and $2$ pairs of brown socks kept together in a box. If he dressed hurriedly in the dark, the probability that after he has put on a black sock, he will then put on another black sock is

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{3}{5}$
• D. $\frac{2}{15}$

Answer 1

The correct option is A $\frac{1}{3}$

Since there are $3$ pairs of black socks this means no. of black socks $=6$
Similarly no. of brown socks $=4$
$P($wearing $1^{st}$ black socks$)$ $=\frac{6}{10}$
$P($wearing $2^{nd}$ black socks$)$ $=\frac{5}{9}$
Hence $P($wearing first black and then again black$)$ $=\frac{6}{10}\times \frac{5}{9}=\frac{1}{3}$