The encounter probability for mountain slope hazards

In typical risk calculations for the mountain slope hazards one wishes to calculate the encounter probability: the probability of facilities or vehicles being hit at least once when exposed for a finite time period L with events having a return period T at a location. In this note, it is assumed that the events are rare, independent, and discrete, with arrival according to a binomial (or Bernoulli) distribution or a Poisson process. The constraints on the formulations for the processes are provided and it is shown that for typical applications either assumption (binomial or Poisson process) may be used in practice almost interchangeably.