The 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

Concept:

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)

= \(1\over 3\) + \(2\over 5\) - \(2\over15\)

= \(11\over15\) - \(2\over15\)

= \(9\over15\)

= \(3\over 5\)