Question
A box contains 4 red, 5 blue, and 3 green balls. Two
balls are drawn at random without replacement. What is the probability that the two balls drawn are of different colours?Solution
ATQ, Total balls = 4 + 5 + 3 = 12. Total ways to draw 2 balls = C(12,2) = 66. Number of ways to draw 2 of the same colour: Red: C(4,2) = 6 Blue: C(5,2) = 10 Green: C(3,2) = 3 Total same-colour ways = 6 + 10 + 3 = 19. Thus different-colour ways = 66 − 19 = 47. Required probability = 47 / 66.
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