Hypergeometric distribution: in the sampling inspection of product quality, if there are m defective products in n products, the number of defective products obtained when sampling n products is X=k, and then P(X=k)=C(M, k) C (n-m, n-k)/C (n, n). At this time, we say that the random variable x obeys hypergeometric distribution, and the model of hypergeometric distribution is not.

Binomial distribution: bernhard test was repeated n times, and the result of random test was expressed by ξ. If the probability of an event is p, then the probability of non-occurrence is q= 1-p, and the probability of occurrence times in n independent repeated experiments is P(x=k)=C(n, k) p k q (n-k), binomial.

When the extraction method is changed from no return to return, the hypergeometric distribution becomes binomial distribution, and when the total number of products n is large, the hypergeometric distribution becomes binomial distribution. The actual prototype of independent repeated test is the sampling inspection with return, but in practical application, the inspection without return with a small number of samples from a large number of products can be regarded as this type approximately.

If you look at it again, it must be that every paragraph is extracted and not put back, so the hypergeometric distribution is adopted.