# Binomial Probability Calculator

**Created By :** Vaibhavi Kumari

**Reviewed By :** Rajashekhar Valipishetty

**Last Updated :** Mar 18, 2023

This Binomial Probability Calculator is a user-friendly probability tool which provides the binomial probability of an event as result by just entering probability of success, number of success, and number of trials in the input field & click the calculate button provided next to the box.

### How to Find Binomial Probability Distribution?

Follow the simple procedure and guidelines mentioned here to find the binomial probability of an event:

- Observe number of trials, number of success, probability of each trial.
- Substitute the values in the binomial probability formula.
- Do the required calculations to get the success binomial probability.

### Define Binomial Probability -- Binomial Probability Formula

When you flip a coin once, you will get either head or tail. The event of getting head is 1/2. The binomial probability is defined as the probability of an experiment that results in exactly two possible outcomes. This experiment is called binomial experiment. The binomial probability distribution refers to the probability of exactly x success for n repeated trials.

The binomial probability formula is given as:

**P(x) = nCx Px qn – x**

Where,

n is the number of trials

P is the probability of success

q is the probability of failure

x is the number of success

**Example**

**Question: Find the binomial probability of random variable r = 4 if n = 10 and p = 0.4.**

Answer:

Given that,

n = 10

p = 0.4

q = 1 – p = 1 – 0.4 = 0.6

r = 4

The formula of binomial probability is P(x) = nCx Px qn – x

P(x = 4) = 10C4 0.44 0.610 – 4

= (10!/4! 6!) × 0.0256 × 0.046656

= 210 × 0.0012

= 0.25

THe binomial probability of the variable is 0.25.

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### FAQ’s on Binomial Probability Calculator

**1. How to solve binomial probability on a calculator?**

Give probability of success, number of trials, number of success details in the input fields and tap on the calculate button to get the binomial probability as result.

**2. What are the 4 requirements for a binomial probability distribution?**

The important four requirements for a binomial probability are here.

- All the observations are independent.
- There should be a fixed number of observations.
- The probability of success for each observation is same.
- Each observation falls into either success or failure.

**3. What is binomial probability formula?**

The binomial probability distribution of exactly x success from n number of trials formula is P(x) = nCx Px qn – x

**4. A coin is tossed 12 times. What is the probability of getting exactly 3 heads?**

The number of trials n = 12

The number of successful trials x = 3

Probability of success in one trial p = 1/2

Probability of failure in one trial q = 1 - 1/2 = 1/2

P(x) = nCx Px qn – x

= 12C3 P3 q12 – 3

= 12!/(3!*(12-3)! 0.53 0.59

= 220 x 0.125 x 0.59

= 0.05371.