The binomial distribution is the discrete probability distribution. It gives you only two possible results in a trial i.e. success or failure. Say, if you gave a test, there are two possibilities of the outcome either pass or fail. The binomial distribution is also represented by a binomial probability distribution.

**n** and **p** are the two significant parameters used in a binomial distribution. N represents the variable that denotes the number of times the trial is done whereas the p variable represents the probability of the favorable outcome.

The binomial distribution calculator is used to solve numerous real-life equations. Some of the concepts that involve the need for a binomial probability calculator are:

Quality inspection: This probability theory is commonly used to find the amount of material before the process and the amount utilized in the making.

Conducting the survey: The binomial distribution is used to conduct surveys where only two outcomes are involved. Say taking the consumers’ reviews on a product that can be positive or negative.

To analyze the performance: The binomial distribution can also be used to analyze the performance of a product or platform. Asking people in yes or no to explain if they like the XYZ tea brand.

Similarly, the binomial distribution can be used in numerous other fields to find out the probability of a desirable outcome.

## The formula used in the binomial distribution calculator:

**P(x = r) = _{n}c_{r }p^{r }(1-p)^{n-r}**

Where,

**n** is no. of trials

**r** is no. of pass or success in the experiment

**P** is the probability of success in every single trial

_{N}c_{r }= (n! / (n-r)! ) / r!

**1-p** is the probability of false or failure

## Condition for conducting binomial probability distribution:

- The number of trials in an experiment are fixed and independent of each other. Each trial in the experiment is an independent trial. The no. of trial in the limited series of an experiment does not depend on each other for its respective outcome.
- The probability of getting any of the outcome (success or failure) varies for each trail.
- There can be only two possible outcomes of the experiment that either success or failure, yes or no, true or false.
- In binomial distribution, only the number of yes is calculated out of the total no. of trials in the experiment.

While running your equation on a binomial distribution calculator make sure it meets the criteria for having fixed no. of trials, independence of each trial, fixed probability of success, and failure in each trial (0.5), and there should be only two mutually exclusive outcomes.