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You have 99 fair coins and one double-headed coin. You pick one at random, flip it k times and see k heads. What is the probability you picked a fair coin?

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Of 1000 coins, one is double-headed and the rest are fair. You pick one at random, flip it 10 times and see 10 heads. What is the probability it is the double-headed coin?You pick at random between a fair coin and a double-headed coin and flip it: heads. If the same coin is flipped again, what is the probability of heads?You see a coin land heads five times in a row. What is the probability it is a two-headed coin?

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