Question
A bag contains 4 red balls, 5 blue balls, and 6 green
balls. Two balls are drawn at random. What is the probability that both balls are of the same color?Solution
Total balls = 4 + 5 + 6 = 15. Total ways to select 2 balls = 15C2 = (15 × 14) / 2 = 105. Favorable outcomes for the same color: Red: 4C2 = (4 × 3) / 2 = 6. Blue: 5C2 = (5 × 4) / 2 = 10. Green: 6C2 = (6 × 5) / 2 = 15. Total favorable outcomes = 6 + 10 + 15 = 31. Probability = 31/105. Correct answer: e.
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