The Rule of Three states that 3/n is an upper 95% confidence bound for binomial probability p when in n independent trials no events occur. We discuss the derivation of this rule, its validity in small samples, and propose some alternatives. The material may serve well as a thought-provoking introduction to a clinical trials, statistical consulting, or a categorical data class, and is interesting on its own merit
A look at the Rule of Three
Jovanovic, BD., & Levy, P. (1997). A look at the Rule of Three. American Statistician, 51(2), 137-139.