Multiple Choice Questions on A speaks truth in 75 cases and B in 80 of the cases In what percentage of cases are they likely to c........... for Study NOtes Preparation

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Multiple Choice Questions

A speaks truth in 75 cases and B in 80 of the cases In what percentage of cases are they likely to c...........

Quantitative Aptitiude (CLAT) Percentage
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    A speaks truth in 75% cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?

    5%

    Incorrect Answer

    15%

    Incorrect Answer

    35%

    Correct Answer

    45%

    Incorrect Answer
    Explanation:
    Let A = Event that A speaks the truth
    B = Event that B speaks the truth
    Then P(A) = 75/100 = 3/4
    P(B) = 80/100 = 4/5
    P(A-lie) = 1-3/4 = 1/4
    P(B-lie) = 1-4/5 = 1/5
    Now
    A and B contradict each other =
    [A lies and B true] or [B true and B lies]
    = P(A).P(B-lie) + P(A-lie).P(B)
    [Please note that we are adding at the place of OR]
    = (3/5*1/5) + (1/4*4/5) = 7/20
    = (7/20 * 100) % = 35%

    By: Amit Kumar
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