What Is a Binomial Experiment?

A binomial experiment is a type of probability distribution in statistics that defines the probability of only two possible outcomes. This experiment involves a specific number of independent trials that lead to exclusively dichotomous alternatives.

A binomial experiment is characterized by four conditions. First, the number of trials must be fixed. Second, each trial should result in only two possible outcomes. In most cases, the first outcome is a success, and the second one is a failure. Third, the probability of each outcome does not change in each and every trial. Finally, the trials must be independent of each other. In other words, the result of one trial should not affect the outcome of the other experiments.

A simple example of a binomial experiment is to check how many heads one flips when a coin is tossed ten times. There are only two possible outcomes to flipping a coin: heads or tails. Out of ten trials, the person doing the experiment must tally the number of times the head side appears. Each of the ten trials does not affect the result of the other coin flips. The probability of getting heads is the same for all trials; there is a 50 percent chance of getting heads and an equal chance of getting tails.

Some more examples include conducting a survey on 100 people to see if they own a car or checking the number of times a four appears when rolling a die.