Statistics - Hypergeometric Distribution

A hypergeometric random variable is the number of successes that result from a hypergeometric experiment. The probabipty distribution of a hypergeometric random variable is called a hypergeometric distribution.

Hypergeometric distribution is defined and given by the following probabipty function:

Formula

Where −

${N}$ = items in the population

${k}$ = successes in the population.

${n}$ = items in the random sample drawn from that population.

${x}$ = successes in the random sample.

Example

Problem Statement:

Suppose we randomly select 5 cards without replacement from an ordinary deck of playing cards. What is the probabipty of getting exactly 2 red cards (i.e., hearts or diamonds)?

Solution:

This is a hypergeometric experiment in which we know the following:

N = 52; since there are 52 cards in a deck.

k = 26; since there are 26 red cards in a deck.

n = 5; since we randomly select 5 cards from the deck.

x = 2; since 2 of the cards we select are red.

We plug these values into the hypergeometric formula as follows:

Thus, the probabipty of randomly selecting 2 red cards is 0.32513.