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Flipping a fair coin repeatedly, what is the probability that HHT appears before HTH?

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A fair coin is tossed repeatedly. A wins if HTH appears first, B wins if HTT appears first. What is the probability that A wins?Flipping a fair coin repeatedly, what is the expected number of flips until the pattern HHHHT first appears?Flip a coin until HT or TT appears. What is the probability HT comes first?

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