- Τhe
**hypergeometric distribution** is a discrete probability distribution that describes the number of successes in a sequence of n draws from a finite population without replacement
- Suppose you are to draw "
**n**" balls without replacement from an basket containing "**N**" **balls** in total, "**m**" of which are **white**. The hypergeometric distribution describes the distribution of the number of white marbles drawn from the urn.
- A random variable X follows the hypergeometric distribution with parameters N, m and n andf the probability is given by :

**For example**, Think an basket wich contains two types of **balls**, blacks and whites. Define drawing a white ball as a success and drawing a black ball as a failure (analogous to the binomial distribution). If the variable *N* describes the number of **all balls in the basket** and *m* describes the number of **white marbles**, then *N* − *m* corresponds to the number of **black balls**.

Now, assume (for example) that there are 5 white and 45 black balls in the basket. Close your eyes and draw **10 balls** without replacement.

What is the probability that exactly 4 of the 10 are white?

The probability is :