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

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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) 𝟐﷮𝟓﷯ 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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