## - Hypergeometric Distribution

Consider a lot consisting of N items of which M of them are defective and the remaining N −M of them are nondefective. A sample of n items is drawn randomly without replacement. (That is, an item sampled is not replaced before selecting another item.) Let X denote the number of defective items that is observed in the sample. The random variable X is referred to as the hypergeometric random variable with parameters N and M . For a given set {N,M,n, k}, the probability P (X = k|n,M,N) is the ratio of the number of samples of size that include exactly k defective items to the possible number samples of size n from the lot. Noting that the number of ways one can select b different objects from a collection of a different objects is (

a

b

) =

a!