Question
In a bag, there are 5 red balls, 6 green balls, and 9
blue balls. If two balls are drawn at random without replacement, what is the probability that both balls drawn are of the same color?Solution
The total number of balls = 5 + 6 + 9 = 20 balls. The total number of ways to choose 2 balls from 20 = C(20, 2) = (20 × 19) / 2 = 190. Now, calculate the number of ways to choose 2 balls of the same color: Red balls: C(5, 2) = (5 × 4) / 2 = 10 Green balls: C(6, 2) = (6 × 5) / 2 = 15 Blue balls: C(9, 2) = (9 × 8) / 2 = 36 Total favorable outcomes = 10 + 15 + 36 = 61. Thus, the probability = 61 / 190 = 3/14. Correct Option: b) 3/14
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