Q. 163.7( 3 Votes )

# The probabilities of A, B, C solving a problem are 1/3, 1/4 and 1/6, respectively. If all the three try to solve the problem simultaneously, find the probability that exactly one of them will solve it.

Given : let A , B and C be three students whose chances of solving a problem is given i.e , P(A) = , P(B) = and P(C) = .

P() = , P() = and P()=

To Find: The probability that excatly one of them will solve it .

Now, P(excatly one of them will solve it) = P(A and not B and not c) +P (B and not A and not C) +P (C and not A and not B)

= P( A ) + P(B ) + P(C )

= P(A) P() P() + P(B) P() P() + P(C) P() P()

= [] + [] + []

= + +

=

Therefore , The probability that excatly one of them will solve the problem is

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