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

Question

Probability of solving specific problem independently by A and B are \(\frac{1}{2}\) and \(\frac{1}{3}\) respectively. If both try to solve the problem independently, find the probability that the problem is 

(i) solved,

(ii) exactly one of them solves the problem.

Answer 1

Given P(A) = \(\frac{1}{2}\) and P(B) = \(\frac{1}{3}\)

(i) The probability that problem is solved = The probability that atleast one solving the problem 

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

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