Expected sets for a favored player

In a best-of-three match, the favorite wins each set independently with probability p=0.6p=0.6. What is the expected number of sets played? Give a decimal to four places.

Show hints (2)+
  1. E[sets]=2+P(first two sets are split)E[\text{sets}] = 2 + P(\text{first two sets are split}).
  2. The split has two orders: 2pq=2(0.6)(0.4)2pq = 2(0.6)(0.4).

Answer

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2.48 (± 0.001)

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Asked at: Options Market-Making, ETF Market-Making

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