# BINOMDIST

The BINOMDIST function calculates the probability of a certain number of successes in a fixed number of trials, where each trial has the same probability of success.

## Syntax

=BINOMDIST(`number_s`

, `trials`

, `probability_s`

, `cumulative`

)

`number_s` | The number of successful outcomes to find the probability for. | ||

`trials` | The number of independent trials. | ||

`probability_s` | The probability of success on each trial. | ||

`cumulative` | A logical value that determines the type of distribution to use. If TRUE | it calculates the cumulative distribution function; if FALSE | it calculates the probability mass function (default). |

## About BINOMDIST

When you find yourself venturing into the world of probability and the likelihood of specific outcomes in a series of trials, turn to the BINOMDIST function in Excel. This powerful tool is particularly valuable in scenarios involving discrete probabilities, such as the success or failure of repeated independent events, making it indispensable in areas like quality control, statistical analysis, and decision-making under uncertainty. By providing the number of successful outcomes, the total number of trials, and the probability of success in each trial, BINOMDIST extends its support in estimating the likelihood of achieving a specific number of successes in the given trials. The optional `cumulative`

argument further enhances its flexibility, allowing users to compute either the probability mass function or the cumulative distribution function based on the logical value specified. In sum, BINOMDIST stands as an essential aid for navigating the probability landscape, offering a clear understanding of the potential outcomes in repetitive, independent trials.

## Examples

Suppose you have a fair coin, and you want to find the probability of getting exactly 3 heads out of 5 flips. The probability of success (getting heads) on each flip is 0.5. To calculate the probability, you can use the formula: =BINOMDIST(3, 5, 0.5, FALSE) This will provide you with the probability of getting exactly 3 heads out of 5 flips.

In another scenario, let's say you're conducting a quality control test, and there's a 20% chance of a defect occurring in each widget produced. If you want to find the cumulative probability of having 2 or fewer defects in a batch of 10 widgets, you can use the formula: =BINOMDIST(2, 10, 0.2, TRUE) This will yield the cumulative probability for having 2 or fewer defects in the given batch of 10 widgets.

## Questions

**What does the cumulative argument in the BINOMDIST function control?**

The cumulative argument in the BINOMDIST function determines the type of distribution to calculate. When set to TRUE, it computes the cumulative distribution function, providing the probability of obtaining up to `number_s`

successful outcomes in `trials`

trials. When set to FALSE (or omitted), it calculates the probability mass function, giving the probability of exactly `number_s`

successful outcomes in `trials`

trials.

**Can I use the BINOMDIST function for continuous probability distributions?**

No, the BINOMDIST function is specifically designed for use with discrete probability distributions, where the outcomes are limited to a fixed number of discrete categories, such as success or failure in a series of independent trials.

**How should I interpret the output from the BINOMDIST function?**

The output of the BINOMDIST function represents the probability of achieving the specified number of successful outcomes in the given number of trials, based on the provided probability of success on each trial. It provides valuable insights into the likelihood of particular outcomes in repetitive, independent events.

## Related functions

POISSON

NEGBINOM.DIST

HYPGEOM.DIST

BINOM.INV