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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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Flip a coin until HT or TT appears. What is the probability HT comes first?Flipping a fair coin repeatedly, what is the expected number of flips until the pattern HHHHT first appears?What is the expected number of fair coin flips needed until the pattern HHT first appears?

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