• Share
Send to a Friend via Email

### Your suggestion is on its way!

An email with a link to:

http://statistics.about.com/od/Formulas/ss/Binomial-Probability-Distribution-Formula.htm

was emailed to:

Thanks for sharing About.com with others!

You can opt-out at any time. Please refer to our privacy policy for contact information.

# Binomial Probability Distribution Formula

Binomial Distribution Formula
C.K.Taylor

The above formula indicates the probability of r successes out of n independent trials, where each success has probability p of occurring.

The formula can be thought of in the following way. The probability of r successes occuring, each with probability p is pr. This leaves n-r failures, and each failure has probability 1-p. We multiply all of these probabilities together because the trials are independent, and this gives us pr(1-p)n-r.

The factorial in the formula shows up because we need to find the combination of ways that we can have r successes out of n trials.

Most calculations involving the binomial distribution will be carried out with software or tables. However, it is important to realize that the values in the table do not fall out of the sky. Only a few mathematical ideas from probability and combinatorics are needed to derive tables of the binomial probability distribution.

Courtney Taylor
About.com Statistics

See More About
Explore Statistics
See More About:
By Category
1. About.com
2. Education
3. Statistics
4. Statistics Formulas
5. Binomial Probability Distribution Formula