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the probability that A solves a problem is 1/2,the probability that B solves the problem is 1/3 and the probability that C solves the problem is 1/4.if the three try to solve the problem independently ,find the probability that exactly one of them solves the problem.
We have P(A) = 1/2 => P(not A) = 1/2,
P(B) = 1/3 => P(not B) = 2/3,
P(C) =1/4 => P(not C) = 3/4.
Probability that only one will solve the problem
= P(A).P(not B).P(not C) + P(not A).P(B).P(not C)+ P(not A).P(not B).P(C)
=1/2x2/3x3/4 + 1/2x1/3x3/4+1/2x2/3x1/4
= 6/24 + 3/24 + 2/24
= 11/24


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