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

Updated On: Jan 30, 2025
  • 518\frac{5}{18}
  • 16\frac{1}{6}
  • 5108\frac{5}{108}
  • 49\frac{4}{9}
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The Correct Option is D

Solution and Explanation

Total ways to choose 2 socks from 9:
(92)=36\binom{9}{2} = 36

Ways to choose 2 brown socks:
(52)=10\binom{5}{2} = 10

Ways to choose 2 white socks:
(42)=6\binom{4}{2} = 6

Total favorable outcomes (same color):
 10+6=1610 + 6 = 16

Probability of same color socks:
 1636=49\frac{16}{36} = \frac{4}{9}

The probability that the two socks are of the same color is 49\frac{4}{9}.

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