### What is hypergeometric distribution?

A hypergeometric distribution, which simulates success rates in a random sample taken from a limited population without replacement, is a probability distribution. It makes the supposition that there are two different kinds of objects in the population: successes and failures.,

### The formula of hypergeometric distribution:

We can calculate the hypergeometric distribution by the following formula:

- N stands for Population size
- K stands for the number of successful states in population.
- (K) Number of success states in the sample.
- n stands for sample size.

### Applications of hypergeometric distribution:

The Hypergeometric distribution has many applications here we discuss some important applications.

- In genetics, the likelihood of finding a specified number of people with a certain genotype in a population is modeled using the hypergeometric distribution.
- It is possible to examine the distribution of species in a certain habitat using the hypergeometric distribution.
- The hypergeometric distribution may be used to simulate the spread of a disease within a population.
- The likelihood that a specific number of deals out of a given number of trades will be successful may be modeled using the hypergeometric distribution in finance.
- In sports, the chance of winning a specific number of games can be determined using the hypergeometric distribution.

### Example section:

In this section, we will solve the step-by-step example of a hypergeometric distribution.

**Example 1:**

Compute the value of hypergeometric distribution when N = 44, K = 22, n = 7, and k = 5.

**Solution:**

First, we find the mean

**Step 1:**

Mean = µ = n × (k / N)

µ = 7 (22 / 44)

µ = 7 × 0.5

µ = 3.5

**Step 2:**

Now we compute the variance

** **σ^{2} = {n × (K / N)} {(N - K) / N} × {(N - n) / (N - 1)}

σ^{2 }= 7× (22 / 44) / × (44−22 / 44) × (44−7/ 44 -1)

σ^{2} = 7 × 0.5 × 0.5 × 0.8605

σ^{2} = 1.5058

**Step 3:**

To Compute the standard deviation, we take the square root of the variance.

√σ^{2} =√ 1.5058

σ = 1.2271

**Step 4:**

Compute the probability

**P (X = k) **

P (X = 5) = 0.1587

**P (X ≥ k):**

P (X ≥ 5) = 0.206

**P (X > k):**

P (X > 5)** **= 0.0473

**P (X ≤ k):**

P (X > 5)** **= 0.9527

**P (X < k):**

P (X < 5)** **= 0.794