Hypergeometric Probability Distribution

Total number in population (N) =

Total sample size (r) =

Items selected from the population (n) =

Random variable (x) =



P(x) =


Hypergeometric Probability Formula

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

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