Hypergeometric Distribution Formula

Hypergeometric distribution is a random variable of a hypergeometric probability distribution. Using the formula of you can find out almost all statistical measures such as mean, standard deviation, variance etc.


N: The number of items in the population.
n: The number of items in the sample.
x: The number of items in the sample that are classified as successes.
P(x| N, n, k): hypergeometric probability – the probability that an n-trial hypergeometric experiment results in exactly x successes, when the population consists of $N$ items, $k$ of which are classified as successes.

Solved Examples

Question 1: Calculate the probability density function of the hypergeometric function if N, n and m are 50, 10 and 5 respectively ?

Given parameters are,
N = 50
n = 10
m = 5

Formula for hypergeometric distribution is,

P(x|N,m,n) = 

P(x|N,m,n) = 

So, the probability distribution function is,

P(x|50, 5, 10) = 

Practise This Question

A mathematician trying to cross a street happened to witness a bank robbery. When the police questioned him, he stated that the number plate of the van in which the thieves escaped had its last four digits as follows:
The first digit is 5. The last digit is the square of the second digit. The third digit is twice the second digit. Also he noticed the sum of digits to be “9”. What is the quadratic equation that the police need to frame to find the 2nd digit, given that ‘b’ is the second digit?