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Question
The probabilities of solving a specific problem independently by A and B are `1/3` and `1/5` respectively. If both try to solve the problem independently, find the probability that the problem is solved.
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Solution
Probability of solving the problem by A, P(A) = `1/3`
P `(\overline"A") = 2/3`
Probability of solving the problem by B, P(B) = `1/5`
P`(\overline"B")= 4/5`
Since the problem is solved independently by A and B,
Probability that the problem is solved = `"P"("A") . "P"(\overline"B") + "P"("B")."P"(\overline"A") + "P"("A")."P"("B")`
` = 1/3 xx 4/5 + 1/5 xx 2/3 + 1/3 xx 1/5`
` = 7/15`
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