What does the hypergeometric probability function compute?

The hypergeometric probability function is specifically designed to calculate the probabilities of obtaining a certain number of successes in a fixed number of draws from a finite population without replacement. This means that the selection of each item affects the probabilities of subsequent selections, which is a key characteristic of the hypergeometric distribution.

In particular, the function allows us to determine the likelihood of achieving exactly a specified number of successes, while taking into consideration both the size of the population and the number of successes present in that population. This contextual setup makes it applicable in scenarios such as drawing colored balls from an urn or selecting defective items from a quality control sample.

This understanding underscores why the answer regarding computing the probabilities of a certain number of successes in a set number of trials from a designated population is the most fitting; it captures both the essence of the hypergeometric function and its practical applications.