## Hypergeometric Distribution Solution

STEP 0: Pre-Calculation Summary
Formula Used
Hypergeometric Probability Distribution Function = (C(Number of Items in Sample,Number of Successes in Sample)*C(Number of Items in Population-Number of Items in Sample,Number of Successes in Population-Number of Successes in Sample))/(C(Number of Items in Population,Number of Successes in Population))
PHypergeometric = (C(mSample,xSample)*C(NPopulation-mSample,nPopulation-xSample))/(C(NPopulation,nPopulation))
This formula uses 1 Functions, 5 Variables
Functions Used
C - In combinatorics, the binomial coefficient is a way to represent the number of ways to choose a subset of objects from a larger set. It is also known as the "n choose k" tool., C(n,k)
Variables Used
Hypergeometric Probability Distribution Function - Hypergeometric Probability Distribution Function is the probability of obtaining a specific number of successes in a sample drawn without replacement from a finite population.
Number of Items in Sample - Number of Items in Sample is the size of the subset or sample that is drawn without replacement from a finite population.
Number of Successes in Sample - Number of Successes in Sample is the count of successes observed when drawing a specific number of elements from a finite population without replacement.
Number of Items in Population - Number of Items in Population is the total count of elements or individuals from which a sample is drawn in the hypergeometric distribution.
Number of Successes in Population - Number of Successes in Population is the count of elements in the finite population that are classified as successes (or the desired outcome) prior to any sampling.
STEP 1: Convert Input(s) to Base Unit
Number of Items in Sample: 5 --> No Conversion Required
Number of Successes in Sample: 3 --> No Conversion Required
Number of Items in Population: 50 --> No Conversion Required
Number of Successes in Population: 10 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
PHypergeometric = (C(mSample,xSample)*C(NPopulation-mSample,nPopulation-xSample))/(C(NPopulation,nPopulation)) --> (C(5,3)*C(50-5,10-3))/(C(50,10))
Evaluating ... ...
PHypergeometric = 0.0441767826464536
STEP 3: Convert Result to Output's Unit
0.0441767826464536 --> No Conversion Required
0.0441767826464536 0.044177 <-- Hypergeometric Probability Distribution Function
(Calculation completed in 00.004 seconds)
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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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## < 4 Hypergeometric Distribution Calculators

Hypergeometric Distribution
Hypergeometric Probability Distribution Function = (C(Number of Items in Sample,Number of Successes in Sample)*C(Number of Items in Population-Number of Items in Sample,Number of Successes in Population-Number of Successes in Sample))/(C(Number of Items in Population,Number of Successes in Population))
Standard Deviation of Hypergeometric Distribution
Standard Deviation in Normal Distribution = sqrt((Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1)))
Variance of Hypergeometric Distribution
Variance of Data = (Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1))
Mean of Hypergeometric Distribution
Mean in Normal Distribution = (Sample Size*Number of Success)/(Population Size)

## Hypergeometric Distribution Formula

Hypergeometric Probability Distribution Function = (C(Number of Items in Sample,Number of Successes in Sample)*C(Number of Items in Population-Number of Items in Sample,Number of Successes in Population-Number of Successes in Sample))/(C(Number of Items in Population,Number of Successes in Population))
PHypergeometric = (C(mSample,xSample)*C(NPopulation-mSample,nPopulation-xSample))/(C(NPopulation,nPopulation))

## What is Probability in Mathematics?

In Mathematics, Probability theory is the study of chances. In real life, we predict chances depending on the situation. But Probability theory is bringing a mathematical foundation for the concept of Probability. For example, if a box contain 10 balls which include 7 black balls and 3 red balls and randomly chosen one ball. Then the Probability of getting red ball is 3/10 and Probability of getting black ball is 7/10. When coming to statistics, Probability is like the back bone of statistics. It has a wide application in decision making, data science, business trend studies, etc.

## What is Hypergeometric Distribution?

The Hypergeometric Distribution is a discrete probability distribution that describes the number of successes in a fixed number of Bernoulli trials (i.e. trials with only two possible outcomes: success or failure) without replacement. The probability mass function (PMF) of the hypergeometric distribution is given by: P(X = x) = (C(K,x) * C(N-K,n-x)) / C(N,n) The Hypergeometric Distribution is used to model the probability of observing a certain number of "successes" in a fixed number of draws from a finite population, where the probability of success changes on each draw. It is used in many fields such as genetics, quality control, and sampling inspection, in which the sample is drawn without replacement.

## How to Calculate Hypergeometric Distribution?

Hypergeometric Distribution calculator uses Hypergeometric Probability Distribution Function = (C(Number of Items in Sample,Number of Successes in Sample)*C(Number of Items in Population-Number of Items in Sample,Number of Successes in Population-Number of Successes in Sample))/(C(Number of Items in Population,Number of Successes in Population)) to calculate the Hypergeometric Probability Distribution Function, The Hypergeometric Distribution formula is defined as the probability of obtaining a specific number of successes in a sample drawn without replacement from a finite population, where each element is classified into one of two categories (success or failure). Hypergeometric Probability Distribution Function is denoted by PHypergeometric symbol.

How to calculate Hypergeometric Distribution using this online calculator? To use this online calculator for Hypergeometric Distribution, enter Number of Items in Sample (mSample), Number of Successes in Sample (xSample), Number of Items in Population (NPopulation) & Number of Successes in Population (nPopulation) and hit the calculate button. Here is how the Hypergeometric Distribution calculation can be explained with given input values -> 0.044177 = (C(5,3)*C(50-5,10-3))/(C(50,10)).

### FAQ

What is Hypergeometric Distribution?
The Hypergeometric Distribution formula is defined as the probability of obtaining a specific number of successes in a sample drawn without replacement from a finite population, where each element is classified into one of two categories (success or failure) and is represented as PHypergeometric = (C(mSample,xSample)*C(NPopulation-mSample,nPopulation-xSample))/(C(NPopulation,nPopulation)) or Hypergeometric Probability Distribution Function = (C(Number of Items in Sample,Number of Successes in Sample)*C(Number of Items in Population-Number of Items in Sample,Number of Successes in Population-Number of Successes in Sample))/(C(Number of Items in Population,Number of Successes in Population)). Number of Items in Sample is the size of the subset or sample that is drawn without replacement from a finite population, Number of Successes in Sample is the count of successes observed when drawing a specific number of elements from a finite population without replacement, Number of Items in Population is the total count of elements or individuals from which a sample is drawn in the hypergeometric distribution & Number of Successes in Population is the count of elements in the finite population that are classified as successes (or the desired outcome) prior to any sampling.
How to calculate Hypergeometric Distribution?
The Hypergeometric Distribution formula is defined as the probability of obtaining a specific number of successes in a sample drawn without replacement from a finite population, where each element is classified into one of two categories (success or failure) is calculated using Hypergeometric Probability Distribution Function = (C(Number of Items in Sample,Number of Successes in Sample)*C(Number of Items in Population-Number of Items in Sample,Number of Successes in Population-Number of Successes in Sample))/(C(Number of Items in Population,Number of Successes in Population)). To calculate Hypergeometric Distribution, you need Number of Items in Sample (mSample), Number of Successes in Sample (xSample), Number of Items in Population (NPopulation) & Number of Successes in Population (nPopulation). With our tool, you need to enter the respective value for Number of Items in Sample, Number of Successes in Sample, Number of Items in Population & Number of Successes in Population and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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