# Cumulative Hypergeometric Distribution Tutorial

## Cumulative Hypergeometric Distribution Tutorial

#### Cumulative Hypergeometric Distribution

##### Definition:

A cumulative hypergeometric distribution is used for calculating the probability of getting atleast n successes in the hypergeometric experiment.

#### Formula:

h(x < x;N;n;k) = h(x = 0;N;n;k) + h(x = 1;N;n;k) +...+ h(x = x;N;n;k)
###### where,

h(x = 0;N;n;k) and h(x = x;N;n;k) is calculated using hypergeometric distribution formula.

##### Example:

Consider, if 5 balls are chosen randomly from the total of 10 balls without repetition. Calculate the probability of getting atleast 2 red balls out of 6 red balls.

###### where,

N=10, n=6, k=5, and x=2. h(x < 2;N;n;k) = h(x = 0;N;n;k) + h(x = 1;N;n;k) + h(x = 2;N;n;k) = [5C0] [5C4] / [10C6] + [5C1] [5C4] / [10C6] + [5C2] [5C4] / [10C6] = 0.001 + 0.024 + 0.238. 0.263. Hence there are 26.3% possibilities for choosing atleast 2 red balls without repetition.

This tutorial will guide you to calculate the cumulative hypergeometric distribution problems.