The binomial distribution can be used to determine probabilities of success for binary variables subjected to a number of trials. Fortunately the binomial distribution is linked to two other probability distributions. The Poisson distribution is associated with events that have a small probability of occurring. It can be used to investigate rare, isolated events which occur at random in time or space.
Animal calls e.g. numbers per unit time.
Incidence of rare diseases. At first this looks a difficult hand calculation. If you know how to use your calculator it is not. Note that, irrespective of the value of X, e - is constant for any particular mean. It's value can be found using an e x function.