# HYPGEOM.DIST

The `HYPGEOM.DIST` function returns the probability of a specified number of successes from a fixed population size, where the sample size is also fixed and drawn without replacement. This function is commonly used in statistics to model experiments where the sample size is small relative to the population size, such as quality control inspections or medical trials.

## Usage

Use the `HYPGEOM.DIST` formula with the syntax shown below, it has 4 required parameters:

Parameters:
1. num_successes (required):
The number of successes in the sample.
2. num_draws (required):
The sample size.
3. successes_in_pop (required):
The number of successes in the population.
4. pop_size (required):
The population size.

## Examples

Here are a few example use cases that explain how to use the `HYPGEOM.DIST` formula in Google Sheets.

### Calculating the probability of getting a certain number of defective products in a sample

A quality control inspector wants to know the probability of finding 2 or fewer defective products in a sample of 10 items randomly selected from a population of 100 items. HYPGEOM.DIST can be used to calculate this probability.

### Modelling the probability of drawing a certain number of red balls from an urn

Suppose there are 10 red balls and 20 blue balls in an urn. If 5 balls are drawn without replacement, what is the probability of getting exactly 2 red balls? HYPGEOM.DIST can be used to calculate the probability.

### Calculating the probability of getting a certain number of successful treatments in a medical trial

Suppose there are 100 patients in a medical trial, 50 of whom receive a new treatment and 50 of whom receive a placebo. If 10 patients are randomly selected to receive the new treatment, what is the probability that exactly 3 will have a successful outcome? HYPGEOM.DIST can be used to calculate the probability.

## Common Mistakes

`HYPGEOM.DIST` not working? Here are some common mistakes people make when using the `HYPGEOM.DIST` Google Sheets Formula:

### Incorrect number of arguments

One of the most common mistakes is providing either too few or too many arguments to the HYPGEOM.DIST formula. Make sure you provide exactly four arguments in the correct order.

### Invalid argument type

Make sure that all the arguments you provide to the HYPGEOM.DIST formula are of the correct type. For example, num_successes, num_draws, successes_in_pop, and pop_size should all be non-negative integers.

### Incorrect order of arguments

Make sure that you provide the arguments to the HYPGEOM.DIST formula in the correct order. The order should be: num_successes, num_draws, successes_in_pop, and pop_size.

The following functions are similar to `HYPGEOM.DIST` or are often used with it in a formula:

• `BINOM.DIST`

The `BINOM.DIST` function returns the probability of a certain number of successes in a fixed number of trials given a probability of success in each trial. It is most commonly used in statistical analysis and hypothesis testing. The function can calculate either the probability mass function (PMF) or the cumulative distribution function (CDF) depending on the value of the `cumulative` parameter.

• `POISSON.DIST`

The `POISSON.DIST` function calculates the Poisson distribution, which is a statistical distribution that shows how many times an event is likely to occur within a specified period of time, given the average rate of occurrence. This function is commonly used in probability theory to model the number of times an event occurs in a fixed interval of time or space. The resulting value represents the probability of the event occurring a certain number of times. If the cumulative argument is set to TRUE (or omitted), the function returns the cumulative distribution function; if set to FALSE, it returns the probability density function.

• `NORM.DIST`

The `NORM.DIST` formula is a statistical function that returns the normal distribution of a specified variable. It is used to determine the probability of a random variable falling within a specified range of values. This function is commonly used in finance and scientific research.

• `T.DIST`

The `T.DIST` function returns the probability of a Student's t-distribution with a specified degrees of freedom. This function is usually used in hypothesis testing to determine the probability that a sample mean is within a specified range of values.

You can learn more about the `HYPGEOM.DIST` Google Sheets function on Google Support.