InterviewSolution
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InterviewSolution
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There are two persons A and B such that the chances of B speaking truth of A and A speaks truth in more than 25% cases. Statement-1: If A and B contradict each other in narrating the same statement with probability `1//2`, then it is certain that B never tells a lie. Statement-2: The probability that A speaks truth is `1//2`.A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True. |
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Answer» Correct Answer - A Consider the following events. E =A speaks truth m, F= B speaks truth ` P (( E cap overlineF) cup ( overlineE cup F)) = 1/2` ` Rightarrow P ( E cap overlineF) + ( overlineE cap F) = 1/2 ` ` Rightarrow P € P (overlineF) + P (overlineE) + (F) = 1/2` ` p xx ( 1-2p) + ( 1 -p) xx 2p = 1/2` ` Rightarrow p -2p^(2) +2p - 2p^(2) = 1/2` ` Rightarrow 8 p^(2) -6p +1 =0` ` Rightarrow ( 4p-1) (2p-1) =0 Rightarrow p =1/2 ` ` P (E) = 1/2` So, statement -2 is ture. Now, ` P(E) = 1/2 Rightarrow P(F) =2p=1 Rightarrow ` is a certain event So, B never tells a lie. Hence, statement -1 is also true and statement -2 is a correct explanation for statement -1 |
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