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.