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Coin A lands heads with probability 2/3 and coin B with probability 1/3. One is chosen at random and flipped three times, all heads. What is the probability it is coin A?

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A coin picked at random from one with P(heads) = 2/3 and one with P(heads) = 1/3 shows three heads in three flips. What is the probability the next flip is heads?I flip three coins and tell you at least one is heads. What is the probability all three are heads?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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