Question

Probabilities of solving a specific problem independently by A and B are 1/2
and 1/3respectively. 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

Given P (A solving the problem) = P (A) = 1212 and P (B solving the problem) = P(B) = 1313.(i) P (the problem is solved)P (problem is solved) = 1 - P (problem is not solved).P (problem is not solved by A) = 1 - P (A solving the problem) = 1 - 12=1212=12P (problem is not solved by B) = 1 - P (B solving the problem) = 1 - 13=2313=23P (neither A nor B solved the problem) = P (problem not solved by A) ×× P (problem not solved by B) = 1212 ×× 2323 = 1313Therefore P (problem is solved) = 1 - 13=2313=23(ii) P (exactly one of them solves the problem)P (exactly one of them solve the problem) = P (A solved the problem but B doesnt) + P (B solved the problem but A doesnt)P (A solved the problem but B doesnt) = P(A) ×× P (B¯B¯) = 1212×× 23=1323=13P (B solved the problem but A doesnt) = P(B) ×× P (A¯A¯) = 1313 ×× 12=1612=16Therefore P (exactly one of them solves the problem) = 13+16=2+16=12