We have n boxes and for i = 1, 2,…, n, the ith box contains ni balls of which ri are white, and the remaining are black. We first select a box and then choose randomly one of the balls in that box. What is the probability that a white ball is selected if

(i) the selection of the box is completely random?

(ii) the probability to select the ith box is pi, for i = 1, 2,…, n, where pi > 0 and p1 + p2 + · · · + pn = 1?