Question

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) = 0.6, 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, x = 3, 4, or 5. (a) Find p(x). x 3 4 5 p(x) (b) Find the expected number of sets required to complete the match for P(A) = 0.6. sets (c) Find the expected number of sets required to complete the match when the players are of equal ability—that is, P(A) = 0.5. sets (d) Find the expected number of sets required to complete the match when the players differ greatly in ability—that is, say, P(A) = 0.9. sets (e) What is the relationship between P(A) and E(x), the expected number of sets required to complete the match? As the probability of winning a single set, P(A), increases from 0.5, the expected number of sets required to complete the match, E(x), decreases. As the probability of winning a single set, P(A), increases from 0.5, the expected number of sets required to complete the match, E(x), increases. As the probability of winning a single set, P(A), increases from 0.5, the expected number of sets required to complete the match, E(x), stays the same.

Answer 1