The Poisson distribution may also be used to find approximate binomial probabilities when nis large and p is small, by letting μ be np. This method provides for faster calculations of probabilities of rare events such as exotic diseases. For example, assume the incidence rate (proportion in the population) of a certain blood disease is known to be 1%. The probability of getting exactly seven cases in a random sample of 500, where μ = np = (0.01)(500) = 5, is
P(Y = 7) = (57 e-5)/7! = 0.1044.
Suppose the incidence of another blood disease is 0.015. What is the probability of getting no occurrences of the disease in a random sample of 200? (Remember that 0! = 1.)