Communications in Information and Systems
Volume 16 (2016)
A note on the number of long runs
Pages: 59 – 81
In this paper we present a simple derivation of the probability of attaining a run of $r$ heads when tossing a coin $n$ times. We use this result to establish other properties of coin tossing. Using the same techniques we find the probability of runs of either heads or tails. We give a complete analysis of both recurrences. In addition we construct the generating functions for the recurrences.