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Flipping a fair coin repeatedly, what is the expected number of flips until the pattern HHHHT first appears?

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What is the expected number of fair coin flips needed until the pattern HHT first appears?Flipping a fair coin repeatedly, what is the probability that HHT appears before HTH?Roll a fair die until a 6 appears. Given that the first 6 came before the first 5, what is the expected number of rolls?

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