Binomial Experiment

A binomial experiment is a probability experiment that has the following three properties.

1. There is a fixed number of independent trials.
2. Each trial has exactly two possible outcomes — success and failure.
3. For each trial, the probability of success is constant.

Details of each property can be seen in the applet by selecting the corresponding number.

The number of successes in a binomial experiment is a random variable that has a binomial distribution.

Example

One of the most well-known examples of a binomial experiment is flipping a coin. There are only two possible outcomes, heads and tales. Either heads or tails could be considered a success, depending on the situation. The outcome of one toss does not impact the probability of the outcome of the next trial.

Extra

An Experiment Reducible to a Binomial Experiment

Note that many probability experiments can be reduced so that they satisfy the conditions of a binomial experiment. In case of rolling a die, there are six possible outcomes. However, they can be divided into two groups — even numbers and odd numbers, for example.

After grouping the outcomes, there are two possible results of each trial — rolling an even number or an odd number. The probability of rolling a number from either group is constant throughout the trials, and the result of rolling the die is not affected by the previous results.

Therefore, rolling a die can also be considered as a binomial experiment as long as success and failure are clearly defined.