Question
A bag contains 5 red balls, 6 blue balls, and 9 green
balls. Two balls are drawn at random without replacement. What is the probability that both balls are of the same color?Solution
Total balls = 5 + 6 + 9 = 20 balls. The number of ways to select 2 balls out of 20 = C(20, 2) = (20 × 19) / 2 = 190. Number of ways to select 2 red balls = C(5, 2) = (5 × 4) / 2 = 10. Number of ways to select 2 blue balls = C(6, 2) = (6 × 5) / 2 = 15. Number of ways to select 2 green balls = C(9, 2) = (9 × 8) / 2 = 36. Total favorable outcomes = 10 + 15 + 36 = 61. Probability = 61 / 190 = 11 / 42. Correct Option: a
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