4. A coin with probability p, where 0 < p

4. A coin with probability $p$, where $0 < p < 1$, of Heads is flipped repeatedly. (a) What is the expected number of flips until the pattern \"HT\" is observed? (b) What is the expected number of flips until the pattern \"HH\" is observed?

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Calvin and Hobbes play a match consisting of a series of games, where Calvin hasA coin with probability p, where 0, of Heads is flipped repeatedly. (a) What is the expected number of flips until the pattern "HT" is observed? (b) What is the expected number of flips until the pattern "HH" is observed? probability p of winning each game and Hobbes has probability q=1-p winning each game (there is no tie for each game). Assume that the games are played independently, and they play with a "win by two" rule: The first player to win two games more than his opponent wins the match. Find the expected number of games played. 4. A coin with probability p, where 0 < p < 1, of Heads is flipped repeatedly (a) (b) What is the expected number of flips until the pattern HT is observed? What is the expected number of flips until the pattern HH is observed?

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4. A coin with probability $p$, where $0 < p < 1$, of Heads is flipped repeatedly. (a) What is the expected number of flips until the pattern \"HT\" is observed? (b) What is the expected number of flips until the pattern \"HH\" is observed?

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