Question

The probabilities of A, B, C solving a problem are $1 third comma space 2 over 7 space and space 3 over 8$ respectively. If all the three try to solve the problem simultaneously find the probability that exactly one of them will solve it.

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Solution

Let E, F, G be the events that A, B, C solve the problem.

therefore space space space straight P left parenthesis straight E right parenthesis space equals space 1 third comma space space straight P left parenthesis straight F right parenthesis space equals 2 over 7 comma space space straight P left parenthesis straight G right parenthesis space equals 3 over 8

straight P left parenthesis straight E with bar on top right parenthesis space equals space 1 minus straight P left parenthesis straight E right parenthesis space equals space 1 minus 1 third space equals space 2 over 3 comma space space straight P left parenthesis straight F with bar on top right parenthesis space equals space 1 minus 2 over 7 space equals 5 over 7 comma space space straight P left parenthesis straight G with bar on top right parenthesis space equals space 1 minus 3 over 8 space equals 5 over 8

P(exactly one solves the problem).

equals space straight P left parenthesis straight E space straight F with bar on top space straight G with bar on top space space or space space straight E with bar on top space straight F space straight G with bar on top space space or space straight E with bar on top space straight F with bar on top space straight G right parenthesis space equals space straight P left parenthesis straight E space straight F with bar on top space straight G with bar on top right parenthesis space plus space straight P left parenthesis straight E with bar on top space straight F space straight G with bar on top right parenthesis space plus space straight P left parenthesis straight E with bar on top space straight F with bar on top space straight G right parenthesis equals space straight P left parenthesis straight E right parenthesis space straight P left parenthesis straight F with bar on top right parenthesis space straight P left parenthesis straight G with bar on top right parenthesis space plus space straight P left parenthesis straight E with bar on top right parenthesis thin space straight P left parenthesis straight F right parenthesis space straight P left parenthesis straight G with bar on top right parenthesis space plus space straight P left parenthesis straight E with bar on top right parenthesis space straight P left parenthesis straight F with bar on top right parenthesis thin space straight P left parenthesis straight G right parenthesis space equals space 1 third cross times 5 over 7 cross times 5 over 8 plus 2 over 3 cross times 2 over 7 cross times 5 over 8 plus 2 over 3 cross times 5 over 7 cross times 3 over 8 space equals 25 over 168 plus 20 over 168 plus 30 over 168 space equals 75 over 168 space equals 25 over 26

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Probability

The probabilities of A, B, C solving a problem are $1 third comma space 2 over 7 space and space 3 over 8$ respectively. If all the three try to solve the problem simultaneously find the probability that exactly one of them will solve it.

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Probability

The probabilities of A, B, C solving a problem are respectively. If all the three try to solve the problem simultaneously find the probability that exactly one of them will solve it.

Some More Questions From Probability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The probabilities of A, B, C solving a problem are $1 third comma space 2 over 7 space and space 3 over 8$ respectively. If all the three try to solve the problem simultaneously find the probability that exactly one of them will solve it.