Hypergeometrisina

Hypergeometrisina is not a recognized term in mathematics or any other established field. It appears to be a neologism or a misspelling. The most likely intended term is "hypergeometric distribution."

The hypergeometric distribution is a discrete probability distribution that describes the probability of obtaining a certain number of successes in a sample of size n drawn without replacement from a finite population of size N that contains exactly K successes. For example, imagine a bag with 10 balls, 3 of which are red. If you draw 5 balls without putting them back, the hypergeometric distribution can tell you the probability of drawing exactly 2 red balls.

The probability mass function for the hypergeometric distribution is given by:

P(X=k) = [C(K, k) * C(N-K, n-k)] / C(N, n)

where C(a, b) represents the binomial coefficient "a choose b."

Key parameters of the hypergeometric distribution are:

N: the population size

K: the number of success states in the population

n: the number of draws (i.e., quantity drawn in each trial)

k: the number of observed successes

The hypergeometric distribution is often used in quality control, survey sampling, and in scenarios where sampling without replacement is inherent. It is closely related to the binomial distribution, but differs in that the probability of success changes with each draw in the hypergeometric case, whereas it remains constant in the binomial case. If the population size N is very large compared to the sample size n, the hypergeometric distribution can be approximated by the binomial distribution.