Binomial Distribution Calculator

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

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 formula of the binomial distribution 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

binomial distribution formula

  • 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.


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.


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 and 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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