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You hold one coin and your opponent two. Each round a coin is flipped: on tails you win one of their coins, otherwise they win one of yours. The first to hold all three wins. What is your probability of winning?

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You flip three coins. What is the probability of exactly two heads given that there is at least one tail?I flip three coins and tell you at least one is heads. What is the probability all three are heads?In a three-flip coin race between Heads and Tails, what is the probability that the side flipped first is behind at the end?

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