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.

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#### Solution

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

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

Since the problem is solved independently by A and B,

1) Probability that the problem is solved = P (A ∪ B)

2)Probability that exactly one of them solves the problem is given by, P(A).P(B') + P(B).P(A')

Concept: Independent Events

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