Question

The probabilities of solving a specific problem independently by A and B are `1/3` and `1/5` respectively. If both try to solve the problem independently, find the probability that the problem is solved.

Answer 1

Probability of solving the problem by A, P(A) = `1/3`

P `(\overline"A") = 2/3`

Probability of solving the problem by B, P(B) = `1/5`

P`(\overline"B")= 4/5`

Since the problem is solved independently by A and B,

Probability that the problem is solved = `"P"("A") . "P"(\overline"B")  + "P"("B")."P"(\overline"A") + "P"("A")."P"("B")`

` = 1/3 xx 4/5 + 1/5 xx 2/3 + 1/3 xx 1/5`

` = 7/15`