# Poisson Probability Calculator

**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.

### 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
^{-λ}λ^{x})/x! - Substitute the values in the above formula and simplify the equation to get the desired output.

**Example:**

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

**Solution:**

Given

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?**

https://www.youtube.com/watch?v=iUVrPHSGY8o

**3. Where to find the Poisson probability calculator online?**

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