Created By : Vaibhavi Kumari
Reviewed By : Rajashekhar Valipishetty
Last Updated : Apr 02, 2023

Take the help of Poisson Probability Calculator and enter the values of mean and no.of occurences in the input boxes then tap on the calculate button to get the desired output and show work in a blink of an eye.

Enter random variable (number of occurences) :
Enter mean (number of occurences) :


What is Meant by Possion Probability ?

A possion probability refers to the probability of acquiring EXACTLY n successes in a poisson experiment where n would be a poisson random variable.

For example, if the receptionist receieved one phone call in an hour. What is the likelihood next hour that she will receive EXACTLY 3 phone calls? The answer of possion probability is getting exactly 3 phone calls in the next hour is 0.061.

Poisson Probability Distribution Formula

In poisson probability, the mean of the distribution is denoted as λ and e is constant where 2.71828 is the approx value. Thus the formula of poisson probability is

P(x, λ ) =(e^– λ * λ^x)/x!

The mean formula in poisson probability distribution is E(X) = λ.

Step by Step Procedure to Find out the Poission Probability Distribution

Process of calculating the poisson probability is explained here in a step-wise manner so that everyone can easily grasp the concept and calculate the poisson probability problems with ease.

  • Firstly, identify or find the mean and no.of exact occurences from the given problem.
  • Once, you get the two values available then apply the formula of poisson probability i.e., P(X = x) = (e λx )/x!
  • Substitute the values in the above formula and simplify the equation to get the desired output.


Doctors check the patients at the rate of 3 per hour. What is the probability of two patients arrivals during the next 30 minutes?



mean (λ) = The arrival rate during 30 minutes = (3/60)*30 = 1.5.

random varaible (n) = 2

The formula of poisson probability is P(x, λ ) =(e^-λ * λ^x)/x!

P(2, 1.5) = e^-1.5 1.5^2 / 2! = 0.251

Therefore, the probability of exactly 2 patients arrivals in the next 30 minutes is 25.1 percent.

FAQs on Free Online Poisson Probability Calculator with Steps

1. What is the poisson probability distribution formula?

The possion probability distribution formula when P(X=x) is as given by P(x; μ) = (e^-μ) (μ^x) / x!.

2. How do you find poisson probability?

When the poisson experiment has an average number of successes within a given region is μ, then the poisson probability can be calculated using the poisson formula. Hence, you can easily calculate the poisson probability distribution.

3. How do you do poisson probability distribution on a calculator TI-84?

3. Where to find the Poisson probability calculator online?

You can find the poisson probability calculator online on official & trusted portal.