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 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
- \(\frac{5}{18}\)
- \(\frac{1}{6}\)
- \(\frac{5}{108}\)
- \(\frac{4}{9}\)
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The Correct Option is D
Solution and Explanation
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 \(\frac{4}{9}\).
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