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Make fair flips from a coin with P(heads) = 1/3, then maximise fair flips obtained per biased flip.

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You have a coin that lands heads with probability 1/3. How do you use it to produce a fair coin flip? If you need many fair flips, how do you make the method efficient, maximising fair flips per biased flip?

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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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