(Solution) - In Exercise 4 92 you found the probability distribution for x -(2025 Original AI-Free Solution)

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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?