The probability of solving particular problems by methods Q and R are 1/2 and 1/3 respectively. Considering this, the problem is solved independently determine the probability the the problem is solved.

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Solution

Given,
P(Q solving the problem) = $\frac{1}{2}$
P(R solving the problem) = $\frac{1}{3}$

P(problem is solved) = 1 - P(problem is not solved)
P(problem is not solved by Q) = $1 - \frac{1}{2} = \frac{1}{2}$

P(problem is not solved by R) = $1 - \frac{1}{3} = \frac{2}{3}$

P(neither Q nor R solved the problem) = P(problem not solved by Q) $\times$ P(problem not solved by R) = $\frac{1}{3}$

Therefore,
P(problem is solved) = $1 - \frac{1}{3} = \frac{2}{3}$

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