# Binomial Distribution Calculator

The binomial distribution calculator calculates the binomial distribution for the given values. The binomial distribution is defined as the probability of exactly x success on n experiments with only two possible outcomes. It is also known as binomial probability.

## What is a Binomial Distribution Calculator?

Binomial Distribution Calculator is an online tool that helps to calculate the binomial distribution. This online binomial distribution calculator helps you to calculate the value of binomial probability in a few seconds. To use this binomial distribution calculator, enter the values given in the input box.

## How to Use Binomial Distribution Calculator?

Please follow the steps below to find the binomial distribution using an online binomial distribution calculator:

**Step 1:**Go to Cuemath’s online binomial distribution calculator.**Step 2:**Enter the probability of success of a single trial, number of successes, and number of trials in the given input boxes.**Step 3:**Click on the**"Calculate"**button to find the value of the binomial distribution.**Step 4:**Click on the**"Reset"**button to clear the fields and enter the different values.

## How Binomial Distribution Calculator Works?

**The binomial distribution** is defined as the probability of getting exactly a specific number of successes in a specific number of trials. To find out the binomial distribution we use the following formula:

b(r; n, P) = ^{n}Cr × P^{r} × (1 – P)^{n – r}

Where b is the binomial probability, n is the number of trials, r is the number of successes, and P is the probability of success of a single trial.

**Solved Example on Binomial Distribution**

A coin is tossed 7 times. What is the probability of getting exactly 4 heads in these 7 tosses and verify it using the binomial distribution calculator?

**Solution:**

Given: Number of trials = 7 and Number of success = 4

Probability of getting heads in a single coin toss = 0.5

Now, probability of getting 4 heads in 7 tosses = b(r; n, P) = ^{n}Cr × P^{r} × (1 – P)^{n – r}

b(4; 7, 0.5) = ^{7}C4 × (0.5)^{4} × (1 – 0.5)^{7 - 4}

b(4; 7, 0.5) = 35 × 0.0625 × (0.5)^{3}

b(4; 7, 0.5) = 2.1875 × 0.125

b(4; 7, 0.5) = 0.2734

Therefore, the probability of getting exactly 4 heads in these 7 tosses is 0.2734

Similarly, you can use the binomial distribution calculator and find the binomial distribution for:

- Number of trails = 15, probability of success of a single trial = 0.4, and number of successes = 5
- Number of trails = 7, probability of success of a single trial = 0.8, and number of successes = 3