Discrete Probability Model Calculators

Use the calculators below to compare and contrast the binomial, Poisson, geometric, and negative binomial probability distribution models.  These calculators illustrate which of these probability models should be chosen for a given probability problem.

Binomial Distribution: used to estimate the number of successes in a fixed number of trials
If you have  trials of a random process, and each trial can be classified as having one of two outcomes (success or failure), and the probability for success is % and is the same for each trial, and the trials are independent, then the probability of getting exactly  successes in 10 trials is 24.609%.  The average number of successes will be 5 with an expected deviation of plus or minus 1.581.

Poisson Distribution: used to estimate how often an event occurs within a specified time or space
If an event occurs on average times per , and the events occur independently of each other, and no two events can happen at exactly the same time, then the probability that the event will happen exactly times in an hour is 3.783%.  On average this event will occur 10.000 times in an hour with an expected deviation of plus or minus 3.162.

Geometric Distribution: used to estimate the number of trials that must occur before the first success
If you are conducting trials of a random process, and each trial can be classified as having one of two outcomes (success or failure), and the probability for success is % and is the same for each trial, and the trials are independent, then the probability of getting the first success on trial number  is 25.000%.  On average, a single success will occur in 2.000 trials with an expected deviation of plus or minus 1.414.

Negative Binomial Distribution: used to estimate the number of trials that must occur before the kth success is observed
If you are conducting trials of a random process, and each trial can be classified as having one of two outcomes (success or failure), and the probability for success is % and is the same for each trial, and the trials are independent, then the probability of getting the th success on the th trial is 8.810%.  On average, there will be 20.000 trials before the 10th success is observed with an expected deviation of plus or minus 4.472.