 # Binomial Distribution Calculator

Input number of events & success, probability of success, and hit calculate button to find binomial distribution

Formula:
P(X = r) = nCr pr (1-p)(n-r)

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Binomial distribution calculator is used to find the binomial distribution of the given terms with steps. This binomial probability calculator follows the binomial distribution formula to calculate it.

## What is binomial distribution?

In statistics, the binomial distribution is a common distribution function for discrete processes in which a fixed probability succeeds for each independently generated value. ## Formula of binomial distribution • n is the total number of events.
• r is the number of successful traces
• p is the success probability.
• 1-p is the failure probability
• nCr is the combination of terms and is equal to `n!/(r! * (n-r)!)`

## How to Calculate the Binomial Distribution?

Follow the below example to learn how to find the binomial distribution.

Example

Find the binomial distribution, if a dice is rolled 7 times with the probability of success is 0.67 if the dice succeed 3 times.

Solution

Step 1: Write the given information.

Number of events = n = 7

Success probability = p = 0.67

Successful trials = r = 3

Step 2: Take the general formula of the binomial distribution.

`P(x=r) = nCr pr (1 – p)n-r`

Step 3: Substitute the given terms in the formula find the combination and simplify the expression.

`P(X=r) = 7C3 (0.67)3 (1 – 0.67)7-3`

= 35 (0.67)3 (1 – 0.67)4

= 35 (0.67)3 (0.33)4

= 35 (0.3008) (0.0119)

`= 0.1253`

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