# Binomial Probability Distribution

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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) (March 2011)

Open content licensed under CC BY-NC-SA

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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.

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