We flip a coin, with success probability $p$, $N$ times. What is the distribution of the number of success runs of length at least $T$?
2026-03-27 02:40:29.1774579229
Number of success runs of length T or more in N coin tosses
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In A First Course in Probability by Sheldon Ross, the author applies inclusion-exclusion formula to do this. First define event $E_i$ as the a sequence of n heads start at position i and followed by a tail. Then find the probability $P(\cup Ei)$.