Suppose two players A and B undertake a series of trials such that each trial independently yields one of the following:
a) a win for A with probability p;
b) a win for B with probability q;
c) a draw (or no result, or a void trial), with probability 1 - p - q.
The game stops at the first win by either A or B.
Answer each of the following questions:
i) What is the probability an that A wins at the nth trial?
ii) What is the probability α that A wins overall?