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

The Correct Option is D

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 \(\frac{4}{9}\).