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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?

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One coin lands heads with probability 2/3 and another with probability 1/3. One is picked at random and flipped three times, giving three heads. What is the probability the next flip is heads?

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