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Mathematics, 24.07.2019 16:10 jells16

You and i play the following game: i toss a coin repeatedly. the coin is unfair and p(h) = p. the game ends the first time that two consecutive heads (hh) or two consecutive tails (tt) are observed. i win if (hh) is observed and you win if (tt) is observed. given that i won the game, find the probability that the first coin toss resulted in head?

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