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`X` speaks truth in 60% and `Y` in 50% of the cases. Find the probability that they contradict each other narrating the same incident.

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X X speaks truth in 60% and Y Y in 50% of the cases. Find the probability that they contradict each other narrating the same incident. A. 1 4 1 B. 1 4 1 C. 1 2 1 D. 2 3 2 Select the correct answer from above options

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Correct Answer - C Consider the following events : A=X speaks truth, B=Y speaks truth. Then, P ( A ) = 60 100 = 3 5 and P ( B ) = 50 100 = 1 2 P Required probability = P ( ( A ∪ ¯¯¯ B ) ∪ ( ¯¯¯ A ∩ B ) ) = P ( A ∩ ¯¯¯ B ) + P ( ¯¯¯ A ∩ B ) P = 3 5 × 1 2 + 2 5 × 1 2 = 1 2 =

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