Binomial Probability Calculator

Binomial probability is defined as the probability of exactly x success on n experiments that has two possible outcomes only.

What is a Binomial Probability Calculator?

'Cuemath's Binomial Probability Calculator' is an online tool that helps to calculate the binomial probability. Cuemath's online binomial probability calculator helps you to calculate the value of binomial probability in a few seconds.

How to Use Binomial Probability Calculator?

Please follow the below steps to find the binomial probability:

• Step 1: Enter the probability of success of a single trial, number of success, and number of trials in the given input boxes.
• Step 2: Click on the "Calculate" button to find the value of binomial probability.
• Step 3: Click on the "Reset" button to clear the fields and enter the different values.

How to Find a Binomial Probability Calculator?

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

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

Solved Example:

A coin is tossed 7 times. What is the probability of getting exactly 4 heads in these 7 tosses?

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) = ⁿCr × P^r × (1 – P)^{n – r}

b(4; 7, 0.5) = ⁷C4 × (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