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The probability that A speaks truth is `(4)/(5)`, while this probability for B is `(3)/(4)`. The probability that they contradict each other when aske

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The probability that A speaks truth is 4 5 , while this probability for B is 3 4 . The probability that they contradict each other when asked to speak on a fact is A. 4 5 B. 1 5 C. 7 20 D. 3 20 Select the correct answer from above options

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Correct Answer - C Consider the following events : E=A speaks truth, F=B speaks truth. We have, P ( E ) = 4 5 and P ( F ) = 3 4 P Required probability = P ( ( E ∩ ¯¯¯ F ) ∪ ( ¯¯¯ E ∩ F ) ) = = P ( E ∩ ¯¯¯ F ) + P ( ¯¯¯ E ∩ F ) = = P ( E ) P ( F ) + P ( ¯¯¯ E ) P ( F ) = = 4 5 × ( 1 − 3 4 ) + ( 1 − 4 5 ) × 3 4 = 7 20 =

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