Hyper Geometric Distribution:

In statistics, a distribution where selections are made from two groups without replacing members of the groups is known as Hyper geometric distribution. Hyper geometric distribution is the probability distribution of a hyper geometric random variable.

Example:

• balls in an urn – either redor green
• a batch of components – either goodor defective

• a population of people – either male or female
• a population of animals in zoo – either tagged or untagged
• voters – either democrats or republicans

A hyper geometric random variable X has the following probability distribution:

P(X=k) =

Where N – population size,

K – Number of successful states in the population,

n – Number of draws or events,

k – Number of successes.

Properties of a hyper geometric experiment are:

• A sample size of n is collected from a population of N without replacement.
• If k is defined as successes in the population N, then (N−k) items will be defined as failures.

Mean =      

Variance =

There are 52 cards in a deck. Find the probability of getting randomly 1 red card out of two cards chosen without replacement.

total population, N = 52(total cards in a deck)

sample population, n = 2( number of cards chosen)

number of successes in total population, K = 26 (number of red cards)

number of successes in draws, k = 1(number of red cards to be chosen)

P(X=1) =  =   = 0.5098

Let us solve this example using Excel function,

HYPGEOMDIST (sample_s,number_sample,population_s,number_population)

Sample_s   is the number of successes in the sample(k).

Number_sample   is the size of the sample(n).

Population_s   is the number of successes in the population(K).

Number_population   is the population size(N).