1. Tennis, Anyone? Two tennis professionals, A and B, are scheduled to play a match; the winner is the first player to win three sets in a total that cannot exceed five sets. The event that A wins any one set is P(A) 5 .6, and is independent of the event that A wins any other set. Let x equal the total number of sets in the match; that is, x53, 4, or 5.

a. Find p(x).

b. Find the expected number of sets required to complete the match for P(A)5.6.

c. Find the expected number of sets required to complete the match when the players are of equal ability—

that is, P(A)5.5.

d. Find the expected number of sets required to complete the match when the players differ greatly in ability—that is, say, P(A)5.9.

e. What is the relationship between P(A) and E(x), the expected number of sets required to complete the match?