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    Question

    There are three people – Axe, Wye and Zed. Probability that Axe speaks the truth is 7/20, probability that Wye speaks the truth is 3/5 and probability that Zed speaks truth is 5/6. For a particular question asked, at most 2 people speak truth. All people answer to a particular question asked.

    What is the probability that Wye will speak truth for a

    particular question asked?
    A 86/119 Correct Answer Incorrect Answer
    B 15/38 Correct Answer Incorrect Answer
    C 14/33 Correct Answer Incorrect Answer
    D 17/40 Correct Answer Incorrect Answer
    E 5/17 Correct Answer Incorrect Answer

    Solution

    In any case Wye speaks truth. Now at most 2 people speaks truth for 1 question. So case (1) : Wye and Axe speaks truth Probability = 3/5 × 7/20 × (1-5/6) = 7/200 Case (2) : Wye and Zed speaks truth Probability = 3/5 × 5/6 × (1-7/20) = 13/40 Case (3) : only Wye speaks truth Probability = 3/5 × (1-5/6) × (1-7/20) = 13/200 Add the three cases, we get = 7/200+  13/40+  13/200  = 7/40

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