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 (i) the problem is solved (ii) exactly one of them solves the problem.

Answer 1

Probability of solving the problem by A, P(A) =  1/2

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

Probability of not solving the problem by A = P(A’) = 1 – P(A) = 1 - 1/2 = 1/2

and probability of not solving the problem by B = P(B’) = 1 – P(B) = 1 - 1/3 = 2/3

(i) P (the problem is solved) = 1 – P(none of them solve the problem) 

=  1 (A' ∩ B') = 1 - P(A')P(B')

(since A and B are independent A’ and B’ are independent)

= 1 - (1/2 x 2/3) = 1 - 1/3 = 2/3

(ii) P (exactly one of them solve the problem) = P(A) P(B’) + P(A’) P(B)

= 1/2 x 2/3 + 1/2 x 1/3 = 1/3 + 1/6 = (2 + 1)/6 = 3/6 = 1/2