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Flip a coin until HT or TT appears. What is the probability HT comes first?

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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 probability that HHT appears before HTH?A fair coin is flipped until HHT or HTT appears. You may bet on either pattern. Which do you pick, and what is each pattern's probability of coming first?

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