A and B flip coins. A starts and continues flippinguntil a

Chapter 3, Problem 3.82

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A and B flip coins. A starts and continues flippinguntil a tail occurs, at which point B starts flippingand continues until there is a tail. Then A takes over, and so on. Let P1 be the probability of thecoins landing on heads when A flips and P2 whenB flips. The winner of the game is the first oneto get(a) 2 heads in a row;(b) a total of 2 heads;(c) 3 heads in a row;(d) a total of 3 heads.In each case, find the probability that A wins.

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