Question

A bag contains $4$ brown and $5$ white socks. A man pulls two socks at random without replacement. The probability that the man gets both the socks of the same colour is

• A. $\frac{5}{108}$
• B. $\frac{1}{6}$
• C. $\frac{5}{18}$
• D. $\frac{4}{9}$

Answer 1

The correct option is D $\frac{4}{9}$

Total number of socks $=9(4B,5W)$
Required probability $=P(B,B)orP(W,W)$
$=P\left(B\right)P\left(B\right)+P\left(W\right)P\left(W\right)$
Probability of pulling a brown socks in first draw is $\frac{4}{9}$
Since, the socks is not replaced, probability of pulling a brown socks in second draw is $\frac{3}{8}$
Probability of pulling a white socks in first draw is $\frac{5}{9}$
Since, the socks is not replaced, probability of pulling a white socks in second draw is $\frac{4}{8}$
Required probability $=\frac{4}{9}\times \frac{3}{8}+\frac{5}{9}\times \frac{4}{8}$
$=\frac{3}{18}+\frac{5}{18}=\frac{4}{9}$