Six heads in a row, what is next?

Question

A fair coin has just landed heads six times in a row. What is the probability that the next flip is also heads?

Accepted Answer

The next flip is heads with probability 	frac12. A coin has no memory: each flip is independent of every flip before it, so the six heads already recorded do not influence the seventh. It is worth separating two different questions. Before you start flipping, the chance of getting six heads in a row is small, \left(	frac12ight)^6 = 	frac{1}{64}. But once those six heads have already happened, they are in the past. The only thing left to resolve is one more independent flip, and that is 	frac12. The urge to say "tails is due now" is the gambler's fallacy: the belief that a fair process k…

Six heads in a row, what is next?

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