What is a Binomial Experiment? Definition and Examples

What is a binomial experiment? A binomial experiment is an experiment that has the following features:

• The experiment has repeated trials

• Each trial has two possible outcomes. One of these two outcomes is called a success and the other is called a failure.

• The probability of success is the same for each trial.

Examples of binomial experiments

Example 1

Tossing a die fifteen times in order to see how many times the die will land on 4 is a binomial experiment.

• The experiment has repeated trials. In this case, the number of trials is fifteen.

• Each trial can either result in a success (The die lands on 4) or a failure (The die lands on 1, 2, 3, 5, or 6). 

• The probability of success is always 1 / 6 each time the die is tossed. 

Example 2

Guessing the answers to ten questions on a true or false test is a binomial experiment.

• The experiment has repeated trials. In this case, the number of trials is ten.

• Each trial can either result in a success (The answer is correct) or a failure (The answer is incorrect). 

• The probability of success is always 1 / 2 each time you guess on a question.