Calvin and Hobbes play a match consisting of a series of games, where Calvin has
Chapter 2, Problem 44(choose chapter or problem)
Calvin and Hobbes play a match consisting of a series of games, where Calvin has probability p of winning each game (independently). They play with a win by two rule: the first player to win two games more than his opponent wins the match. Find the probability that Calvin wins the match (in terms of p), in two dierent ways: (a) by conditioning, using the law of total probability. (b) by interpreting the problem as a gamblers ruin problem.
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