A bag contains 5 black and 4 white balls. A man selects two balls at random. What is the probability that both of these are of the same colour?
- A. \frac{1}{6}
- B. \frac{5}{108}
- C. \frac{4}{9} ✓
- D. \frac{5}{18}
Correct Answer: C. \frac{4}{9}
Explanation
Probability of selecting 2 balls of the same color = P(\text{both black}) + P(\text{both white}) = \frac{\binom{5}{2}}{\binom{9}{2}} + \frac{\binom{4}{2}}{\binom{9}{2}} = \frac{10}{36} + \frac{6}{36} = \frac{16}{36} = \frac{4}{9}.
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