22. Suppose that two teams play a series of games that ends when one of them has...
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22. Suppose that two teams play a series of games that ends when one of them has won i games. Suppose that each game played is, independently, won by player A with probability p. Find the expected number of games that are played when
(a) i = 2 and
(b) i = 3. Also show in both cases that this number is maximized when p = $\frac{1}{2}$.
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