Qm
Probability

Flips until two heads in a row on a lucky coin

waiting-timeconsecutive-runs

A biased coin lands heads with probability 2/32/3 on each flip. You flip until you see 22 heads in a row; any tail resets your current head streak 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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