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    Question

    A box contains 5 red balls, 3 blue balls and 2 green

    balls. Two balls are drawn at random without replacement. What is the probability that both balls are of different colours?
    A 33/27 Correct Answer Incorrect Answer
    B 23/45 Correct Answer Incorrect Answer
    C 31/45 Correct Answer Incorrect Answer
    D 58/33 Correct Answer Incorrect Answer

    Solution

    ATQ, Total balls = 5 + 3 + 2 = 10 Total ways to choose 2 balls = C(10, 2) = 45 Ways to get both of same colour: Red–Red: C(5, 2) = 10 Blue–Blue: C(3, 2) = 3 Green–Green: C(2, 2) = 1 Total same-colour ways = 10 + 3 + 1 = 14 So different-colour ways = 45 − 14 = 31 Required probability = 31/45

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