Independent trials, resulting in one of the outcomes 1, 2, 3 with respective probabilities p1,p2,p3,

3 i=1 pi = 1, are performed.

(a) Let N denote the number of trials needed until the initial outcome has occurred exactly 3 times. For instance, if the trial results are 3, 2, 1, 2, 3, 2, 3 then N = 7. Find E[N].

(b) Find the expected number of trials needed until both outcome 1 and outcome 2 have occurred.