Question: Successively flip a (fair) quarter until the pattern HHHT appears, that is, until you observe three successive heads followed by a tails. In order to

Successively flip a (fair) quarter until the pattern HHHT appears, that is, until you observe three successive heads followed by a tails. In order to calculate some properties of this game, define a Markov chain with the following states: 0, H, HH, HHH, and HHHT, where 0 represents the starting point, H represents a single observed head on the last flip, HH represents two successive heads on the last two flips, HHH represents three successive heads on the last three flips, and HHHT is the sequence that you are looking for. Find the transition probability matrix.

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