Probability of solving specific problem independently by A and B are $\large \frac{1}{2}$ and $\large \frac{1}{3}$ respectively. If both try to solve the problem independently, find the probability that $\text {(i) the problem is solved (ii) exactly one of them solves the problem.}$

Question

$\begin{array}{1 1}(i) 2/3 (ii) 1/2 \\(i) 1/2 (ii) 2/3\\ (i) 1/3 (ii) 1/2 \\ (i) 1/3 (ii) 2/3 \end{array}$