Two players, A and B, alternately and independently flip a coin and the first player to obtain a head wins. Assume player A flips first.
(a) If the coin is fair, what is the probability that A wins?
(b) Suppose that P(head) = p, not necessarily 1/2. What is the probability that A wins?
(c) Show that for all p, 0 < p < 1,P(A wins) > 5. (Try to write P(A wins) in terms of the events E1, E2,..., where Ei = {head first appears on ith toss}.)