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Question
A Problem in Mathematics is given to the three students A, B and C. Their chances of solving the problem are `1/2, 1/3` and `1/4` respectively. Find the probability that exactly two students will solve the problem.
Solution
Given probabilities of solving a problem by A, B and C are
P(A) = `1/2`,
P(B) = `1/3`
and P(C) = `1/4`
`\implies "P"(bar"A") = 1 - 1/2 = 1/2`,
`"P"(bar"B") = 1 - 1/3 = 2/3`
and `"P"(bar"C") = 1 - 1/4 = 3/4`
Probability of solving the problem by exactly two students
= `"P"("A")"P"("B")"P"(bar"C") + "P"("A")"P"(bar"B")"P"("C") + "P"(bar"A")"P"("B")"P"("C")`
= `1/2 xx 1/3 xx 3/4 + 1/2 xx 2/3 xx 1/4 + 1/2 xx 1/3 xx 1/4`
= `(3 + 2 + 1)/24`
= `6/24`
= `1/4`
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