Question
Download Solution PDFThe probability of solving a problem by A and b individually are \(1\over 3\) and \(2\over 5\). Then the probability that the problem is solved is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If P(A) and P(B) is the probability of occurring any event independently, then P(A ⋃ B) = P(A) + P(B) - P(A ⋂ B)
Calculation:
Probability of the problem being solved by A, P(A) = \(1\over 3\)
Probability of the problem being solved by B, P(B) = \(2\over 5\)
P(AB) = \({1\over 3}\times {2\over 5}\) = \(2\over15\)
Then the probability that the problem is solved is
P(A ⋃ B) = P(A) + P(B) - P(AB)
= \(1\over 3\) + \(2\over 5\) - \(2\over15\)
= \(11\over15\) - \(2\over15\)
= \(9\over15\)
= \(3\over 5\)
Last updated on Jul 4, 2025
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