Question

Probability of solving specific problem independently by A and B are `1/2` and `1/3` respectively. If both try to solve the problem independently, find the probability that

1. the problem is solved
2. exactly one of them solves the problem.

Answer 1

According to the question, P(A) = `1/2`, P(B) = `1/3`

∴ `"P"(overline"A") = 1 - "P"("A") = 1 - 1/2 = 1/2`

and `"P"(overline"B") = 1 - "P"("B") = 1 - 1/3 = 2/3`

i. ∴ Probability that the problem is not solved by both = `"P"(overlineA ∩ overlineB) = P(overlineA) . P(overlineB)`

= `1/2 xx 2/3`

= `1/3`

∴ The probability that at least one solves the problem

= `1 - P(overlineA ∩ overlineB)`

= `1 - 1/3`

= `2/3` 

ii. The probability that only one person will solve the problem

= P(A ∩ B') + P(A ∩ B')

= P(A) . P(B') + P(A') . P(B)

= `1/2 xx 2/3 + 1/2 xx 1/3`

= `2/6 + 1/6`

= `3/6`

= `1/2`