Binomial Probability Distribution

In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of independent binary (yes/no) experiments, each of which yields success with probability . Move the sliders to control the number of trials (or experiments) and the probability of success to see the probability of each of the possible values of the binomial random variable.
  • Contributed by: Paul Savory (University of Nebraska — Lincoln)



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Suppose an experiment conforms to the following requirements: (1) the experiment consists of trials, where is fixed before the start of the experiment; (2) the trials are independent Bernoulli experiments (i.e., each trial results in either a success or failure); (3) the trials are independent, so that the outcome of any particular trial does not influence the outcome of any other trial; and (4) the probability of success is constant from trial to trial and is denoted by . An experiment that satisfies conditions (1) to (4) is called a binomial experiment. Given a binomial experiment consisting of trials, the probabilities that the binomial random variable associated with this experiment takes on values in its range can be found using the binomial probability function . This Demonstration shows these probabilities for a user-specified value of the number of trials or experiments and the probability of success for a trial.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Related Curriculum Standards

US Common Core State Standards, Mathematics

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+