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 at least two of them will solve the problem.

Answer 1

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 at least two of them

= `"P"("A")"P"("B")"P"(bar"C") + "P"("A")"P"(bar"B")"P"("C") + "P"(bar"A")"P"("B")"P"("C") + "P"("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) + (1/2 xx 1/3 xx 1/4)`

= `(3 + 2 + 1 + 1)/24`

= `7/24`