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Question

Probability of solving specific problem independently by A and B are 12 and 13 respectively. If both try to solve the problem independently, find the probability that the problem is solved.

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Solution

Let A be the event of solving the problem by A and B be that of B.
Then according to the problem,
P(A)=12 and P(B)=13.
Now if they solve the problem independently then the probability of solving the problem is
P(AB)
=P(A)+P(B)P(AB)
=P(A)+P(B)P(A).P(B) [ Since A and B are independent]
=12+1312.13
=5616
=46
=23.

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