The Relationship Between the Binomial and Poisson Distributions
A look at the relationship between the binomial and Poisson distributions (roughly, that the Poisson distribution approximates the binomial for large n and small p). I work through some calculations in an example, showing that the approximate probability from the Poisson can be quite close to the exact probability from the binomial distribution.
(The example used involves albinism. Albinism affects all races, but the rates of albinism vary a little around the world. In Europe and North America, roughly 1 in 20,000 people have some form of albinism).
For those using R, here is the R code to find the probabilities for the example in this video:
Finding the probability of getting exactly 2 with albinism in a random sample of 1000 Europeans.
Binomial (exact):
dbinom(2,1000,1/20000)
[1] 0.001187965
Poisson (approximate):
dpois(2,1000*1/20000)
[1] 0.001189037
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