The encounter probability for mountain slope hazards

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