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    Question

    Amar tells the truth in 75% of cases and Akbar in 25% of

    cases.Find the probability that at least one of them tells the truth in a trial.
    A 17/20 Correct Answer Incorrect Answer
    B 12/11 Correct Answer Incorrect Answer
    C 13/16 Correct Answer Incorrect Answer
    D 20/21 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Amar tells truth = 0.75

    → lies = 0.25

    Akbar tells truth = 0.25

    → lies = 0.75

    At least one truth:

    P = 1 – P(both lies)

    P(both lies) = 0.25 × 0.75 = 0.1875

    P(at least one truth) = 1 – 0.1875 = 0.8125 = 13/16

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