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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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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?If you flip a coin 10 times and the results are all heads, what’s the probability that the coin is a fair coin?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?

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