Question
A bag contains 5 red balls, 7 blue balls, and 8 green
balls. Two balls are drawn at random. What is the probability that both balls drawn are of the same color?Solution
Total balls = 5 + 7 + 8 = 20. Total ways to draw 2 balls = C(20, 2) = 20 × 19 / 2 = 190. For red balls: Ways to choose 2 red balls = C(5, 2) = 5 × 4 / 2 = 10. For blue balls: Ways to choose 2 blue balls = C(7, 2) = 7 × 6 / 2 = 21. For green balls: Ways to choose 2 green balls = C(8, 2) = 8 × 7 / 2 = 28. Total favorable outcomes = 10 + 21 + 28 = 59. Probability = 59 / 190 Correct answer: d.
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