# Hypergeometric Probability Distribution

### Hypergeometric Probability Formula

Where:

N is the population size (total number of items in the problem)

r is the number of successes in the population (also referred to as subpopulation)

n is the number of draws (items selected)

x is the number of observed successes (we are looking for the probability of x occurring)

The following is a very good, and detailed, explanation of how to solve a hypergeometric probability distribution problem.

### Hypergeometric Probability Sample Problem

Chase has a deck of cards (there are 52 cards in a deck). Suppose he randomly selects 7 cards without replacing then. What is the probability of getting exactly 3 black cards (either a club or a spade).In this example, the variables are set up in the following way:

N : 52 total cards in the deck (population)

r : 26 cards from the sample (26 are black, 26 are red)

n : 7 cards randomly selected from the deck (population)

x : 3 cards are the random variable (3 black cards)

The probability of randomly selecting 3 black cards is: .2905