Question
Probabilities of solving a specific problem independently by A and B are 
respectively. If both try to solve the problem independently, find the probability:
(i) the problem is solved (ii) exactly one of them solves the problem.
Solution
(i) The probabilities of A and B solving the problem are 
respectively.
i.e.
the probabilities of A and B solving the problems are 
i.e.,
respectively.
probability that problem is not solved by A and B = 
probability that the problem is solved = 
(ii) P(exactly one of them solves the problem)
respectively. i.e.
the probabilities of A and B solving the problems are i.e.,
respectively. probability that problem is not solved by A and B = probability that the problem is solved = (ii) P(exactly one of them solves the problem)
