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    Question

    Roger Federer gets a chance of 60% to win 1st set of tennis and Andy Murray gets a chance of 55% to win 2nd set of tennis. In what Percent of cases are they likely to contradict each other, narrating the same incident?

    A 38% Correct Answer Incorrect Answer
    B 78% Correct Answer Incorrect Answer
    C 49% Correct Answer Incorrect Answer
    D 58% Correct Answer Incorrect Answer
    E 64% Correct Answer Incorrect Answer

    Solution

    Let ‘A’ be the event that Roger Federer wins 1st set. Let ‘B’ be the event that Andy Murray wins 2nd set. Then, A’ = Event that the Roger Federer losses 1st set And B’ = Event that the Andy Murray losses 2nd set. Therefore, P(A) =60/100 = 12/20 P(B) = 55/100 = 11/20 P(A’) = 1 – (12/20) = 8/20 P(B’) = 1 – (11/20) = 9/20 First, we have to find the probability that they contradict each other. That is, P(A and B contradicts each other) = P[(Roger Federer win in 1st set and Andy Murray losses in 2nd set) (or) (Roger Federer losses in 1st set and Andy Murray wins in 2nd set)] =P(A) × P(B’) + P(A’) × P(B) = 12/20  ×  9/20+  11/20  ×  8/20 = 196/400 Required Percentage = 196/400  ×100 = 49%

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