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GATE-MT-2019-->View question

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Here are three possible cases:
Case 1 : Only A solves the problem
Case 2 : Only B solves the problem
Case 3 : Both A and B solves problem
P(Only A solves the problem) = P(A solving the problem) x P( B not solving the problem)  -(1)
P(Only B solves the problem) = P(B solving the problem) x P( A not solving the problem)   -(2)
P(Both A and B solves the problem) = P(A solving the problem) x P( B solving the problem)   -(3)
P(atleast one of them solve the problem ) = P(Only A solves the problem) + P(Only B solves the problem) + P(Both A and B solves the problem)
= 1/3 x 3/5 + 2/5 x 2/3 + 1/3 x 2/5

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