Individuals A and B begin to play a sequence of chess games. Let S = {A wins a game}, and suppose that outcomes of successive games are independent with P(S) = p and P(F) = 1 - p (they never draw). They will play until one of them wins ten games. Let X = the number of games played (with possible values 10, 11,..., 19).
a. For x = 10, 11, ..., 19, obtain an expression for p(x) = P(X = x).
b. If a draw is possible, with p = P(S), q = P(F), 1 - p - q = P(draw), what are the possible values of X? What is P(20 < X)? [Hint: P(20 < X) = 1 - P(X , 20).]