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# Communications in Information and Systems

## Volume 16 (2016)

### Number 1

### A note on the number of long runs

Pages: 59 – 81

DOI: http://dx.doi.org/10.4310/CIS.2016.v16.n1.a3

#### Authors

#### Abstract

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.