Tennis, again In Exercise 4.92 you found the probability distribution for x, the number of sets required to play a best-of-five-sets match, given that the probability that A wins any one set—call this P(A)—is .6.
a. Find the expected number of sets required to complete the match for P(A) = .6.
b. Find the expected number of sets required to complete the match when the players are of equal ability—that is, P(A)= .5.
c. Find the expected number of sets required to complete the match when the players differ greatly in ability—that is, say, P(A) = .9.
d. What is the relationship between P(A) and E(x), the expected number of sets required to complete the match?
Reference:
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 independent of the event that A wins any other, and the probability that A wins any one set is equal to .6. Let x equal the total number of sets in the match; that is, x = 3, 4, or 5. Find p(x).
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