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 the problem is

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

Answer 1

Given P(A) = `1/2` and P(B) = `1/3`

i. The probability that problem is solved = The probability that at least one solving the problem

= 1 – P(none of them solving the problem)

= `1 - "P"(bar"A" ∩ bar"B")`

= `1 - "P"(bar"A") xx "P"(bar"B")`

= `1 - (1 - 1/2) xx (1 - 1/3)`

= `1 - (1/2) xx (2/3)`

= `1 - 1/3`

= `2/3`

ii. P(exactly one of them solves the problem)

= `"P"(bar"A" ∩ "B") + "P"("A" ∩ bar"B")`

= `"P"(bar"A") xx "P"("B") + "P"("A") xx "P"(bar"B")`

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

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

= `1/6 + 2/6`

= `3/6`

= `1/2`