Qm
Probability

Flips until three of the same face in a row

waiting-timeconsecutive-runs

You flip a fair coin until you see 33 of the same face in a row, that is, either HHH or TTT. A flip that differs from the one before it starts a brand-new streak of length 11 (it is not a full reset to zero).

On average, how many flips does that take?

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The theory behind this question.

The Exponential DistributionThe Geometric DistributionThe Negative Binomial DistributionThe M/M/1 Queue and Waiting-Time DistributionsThe ABRACADABRA Problem

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