Ex 13.3, 13 - Probability that A speaks truth is 4/5. A coin - Bayes theorem

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Ex 13.3, 13 Probability that A speaks truth is 4 5 . A coin is tossed. A reports that a head appears. The probability that actually there was head is (A) 4 5 (B) 1 2 (C) 1 5 (D) Let E : A speaks truth F : A Lies H : head appears on the toss of a coin We need to find the Probability that head actually appears, if A reports that a head appears i.e. P(E|H) P(E|H) = P(E) . P(H|E) P(F) . P(H|F) + P(E) . P(H|E) Putting values in formula, P(E|H) = 4 5 1 2 1 5 1 2 + 4 5 1 2 = 1 5 1 2 4 1 5 1 2 [1+4] = 4 5 Therefore, required probability is 4 5

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