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    Question

    Out of 36 balls in a bag, some are black and the rest

    are white in the ratio 7:5. Two balls are drawn randomly without putting back the first one. What is the probability that both drawn balls are of the same colour?
    A 5/7 Correct Answer Incorrect Answer
    B 2/37 Correct Answer Incorrect Answer
    C 1/2 Correct Answer Incorrect Answer
    D 3/14 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ.

    The number of black balls = 36 × (7/12) = 21 The number of white balls = 36 - 21 = 15 So, the probability that both the balls are black = {²¹C₂ / ³⁶C₂} So, the probability that both the balls are white = {¹⁵C₂ / ³⁶C₂} So, required probability = {²¹C₂ / ³⁶C₂} + {¹⁵C₂ / ³⁶C₂} = (210 + 105) / 630 = 315/630 = 1/2

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