Difference Between Bernoulli and Binomial

By: | Updated: Oct-16, 2022
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Bernoulli and binomial are both mathematical terms. They are used in probability theory. These two terms have different meanings, but they both have the same appearance and usage. They both appear in different places in the subject.

Summary Table

Bernoulli Binomial
States that there is a limited outcome of one trial States that there are only two outcomes of one trial
The number of outcomes depends on the trial itself The number of outcomes is fixed

Difference Between Bernoulli and Binomial


Bernoulli is characterized by having a very small probability of certain events happening to any of its predicted outcomes. This means that it deals with discrete.

A discretion variable indicates a variable that has fewer or fewer values than other variables. For example, the number of heads you get if you toss three coins at a time or the number of students in a class.

In statistics and probability, the binomially-shaped distribution shows how many probability combinations are in a given experiment, allowing us to predict whether the experiment will be successful or not.

If one of us tosses a piece of paper, it is likely to result in one of two things: heads or tails. If a certain test is administered, it is very likely to give one of two outcomes: passing or failing.

This type of distribution, which is frequently used to describe probabilities in probability, is known as a binomial probability distribution.

Difference Between Bernoulli and Binomial

The main difference between the two terms is that Bernoulli distribution is used to describe the frequency of occurrence of a certain event. This is while Binomial distribution is used to describe the probability of two events happening in a particular sequence.

Bernoulli believes that there is a limited probability of the event occurring in any particular sequence. This is also known as “independent trials”. Meanwhile, Binomial believes that there are only two possible outcomes and that the probability of both outcomes happening is the same.

If we assume that a Bernoulli event occurs only once, the distribution of the Bernoulli random variable is a binomial distribution with n trials.

Similarly, if we assume that a Binomial event occurs only once, then the probability of two Binomial events occurring in a particular sequence is also given by the binomial distribution.

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