Binomial Distribution Calculator

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
• ⁿC_r 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