There has been some recent concern in the orbital debris scientific community over whether the Poisson probability density function is valid for the present-day studies involving larger debris fluxes, longer duration missions, and larger cross sectional areas. This paper presents the mathematical definitions for Poisson and its more physically founded cousin, the binomial distribution, and discusses the relationship between them. The debris impact problem is then formulated using both distributions, and a quantitative comparison is presented along with several examples. It is concluded that although the orbital debris collision problem is inherently binomial, one often does not have the necessary knowledge to accurately formulate the binomial expression. Furthermore, Poisson provides probability estimates that, for a wide range of studies, approximates those of the binomial very well.