# Hypergeometric Probability Distribution Calculator

Total number in population (N) =

Total sample size (r) =

Items selected from the population (n) =

Random variable (x) =

Solution

P(x) =

## Hypergeometric Probability Formula

$\LARGE P(x)=\frac{_{r}C_{x}_{N-}_{r}C_{n}_{-x}}{_{N}C_{n}}$

## Hypergeometric Probability Sample Problem

Chase has a deck of cards (there are 52 cards in a deck). Suppose he randomly selects 9 cards without replacing them. What is the probability of getting exactly 4 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 : 9 cards randomly selected from the deck (population)
x : 4 cards are the random variable (4 black cards)

The probability of randomly selecting 4 black cards is: .2673

Below is a really good explanation of how to solve Hypergeometric Distribution problems

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