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Question: consider a markov chain which keeps track of the consecutive...

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Consider a Markov Chain which keeps track of the consecutive number of wins currently obtained when independent rounds of a game are played where at each round the probability of winning is p. The game ends as soon as three consecutive wins have been obtained. This Markov Chain has four states 10, 1, 2, 3] representing the current number of consecutive wins with transition matrix q 0 p 0 q 0 0 p 0 0 0 1 Suppose p- 18/38 (this is the probability of winning a bet on red in Roulette). Given that your current state is X-2 what is the probability that you will have a success run of length 3 within the next five rounds?

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