# Hypergeometric Probability Distribution

### Hypergeometric Probability Formula

### 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