# Binomial Distribution: What It Is and Need of Binomial Probability Calculator

Having doubts about what is binomial probability and how you can use it on a calculator. Here we are offering an answer to most of the quires related to binomial probability calculation:

## What is the binomial probability?

The binomial probability or binomial probability distribution is a significant probability distribution model that is used when you are expecting two possible outcomes (binomial) from a set of data e.g. probability of a student named Rahul, failing or passing in 10 subjects. In a condition where more than two distinct outcomes are expected a multinomial probability distribution is used e.g. probability of outcomes of 3, 6, and 5 when a dice is thrown **10** times.

The two expected outcomes are denoted as success and failure respectively. The success indicates the outcome of interest whereas failure is the other expected result that is not favorable. The binomial probability distribution allows us to calculate the chances of observing a total number of successes when a test is repeated number of times. Here, the outcomes of the test are either success or failure. You can use a binomial probability calculator to get your data results instantly.

**What is the formula for binomial probability distribution?**

The formula for binomial distribution is:

**b(x;n,P)=nCX*Px * (1-P)n-x**

here;

**B **= Binomial Probability

**X** = total no. of success

**P** = Probability of success outcomes

**n** = total no. of trials

The binomial distribution can also represent in another way where:

**nCx = n!/x!(n-x)!** (in this formula binomial formula factorials are used.

**P(X) = n! / (n – X)! X! *(p)X * (q)n-X**

Here **q** is the probability of failure (subtracting the probability of success from 1)

## What is the key difference between normal and binomial distribution?

The main difference that separates normal distribution from binomial distribution is the discrete nature of binomial probability distribution. This explains that in the case of binomial probability there are no other observation points among the two defined data points. On the other hand in the case of the normal distribution, there are continuous data points.

The events of the binomial distribution are finite or limited whereas, the normal distribution has an infinite number of events.

## What is the example binomial probability?

Many real-life examples involve the use of the binomial probability formula to predict the result. For example, a new cancer-curing drug is given to a group of ill people. The drug will either work or not.

Example of using binomial distribution with first mentioned formula: **b(x;n,P)=nCX*Px * (1-P)n-x**

A dice is rotated **10** times what is the probability of getting **1 for 6** times?

The number of trails **n = 10**

The odds of success (getting 1 than any other number) is **0.5 (so 1-p = 0.5)**

**X** = 6

**P(x=6) = 10C6 * 0.5^4 = 210 * 0.015625 * 0.0625 = 0.205…..**

## What are the requirements for binomial distribution?

To condition binomial distribution formula for your set of data it has to satisfy four significant conditions:

- The test or observation must consist of n fixed or identical trials
- Each observation must result in only one of two outcomes i.e. Success and failure.
- The number of trials should be independent of each other. This means the outcome of any observation must be independent and does not affect the result of any other trial.
- The probability of success i.e. p must remain constant. That is the probability of success should stay the same from observation to observation.

The binomial distribution can be used to solve numerous day to day tasks that involve discrete result i.e. either true or false. To gain the correct result you need to implement your formula in the right direction which might go wrong while solving the equation manually. However, using a binomial distribution calculator can make the task quite easy and seamless.

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