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A run is a sequence of adjacent '0's or '1's. If a sequence of random Bernoulli variables is drawn independently, after drawing a first '0'

A run is a sequence of adjacent '0's or '1's.

If a sequence of random Bernoulli variables is drawn independently, after drawing a first '0' or '1', what is the probability that the first run will be of length 1?

What is the probability that the first run will be of length 2?

What is the probability that the first run will be of lengthk?

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