Question

A box contains 5 brown and 4 white socks. A man takes out two socks. The probability that they are of the same colour is

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

Answer 1

Answer: (D)

$\frac{4}{9}$

Answer 2

Total ways to choose 2 socks from 9:
$\binom{9}{2} = 36$

Ways to choose 2 brown socks:
$\binom{5}{2} = 10$

Ways to choose 2 white socks:
$\binom{4}{2} = 6$

Total favorable outcomes (same color):
$10 + 6 = 16$

Probability of same color socks:
$\frac{16}{36} = \frac{4}{9}$

The probability that the two socks are of the same color is $\frac{4}{9}$.