# Binomial Experiments: Definition, Characteristics & Examples

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• 0:03 Binomial Experiments
• 0:45 Understanding Binomial…
• 2:25 Identifying Binomial…
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Binomial experiments happen in your everyday life far more often than you might think. In this lesson, you will learn the characteristics of binomial experiments that will help you identify them.

## Binomial Experiments

Zoey has a long-standing tradition with her brother, Gabe. When it is time to take out the trash, they flip a coin to see who is responsible. If it is heads, then Zoey has to take the trash out; if it is tails, then Gabe has to take the trash out. Although the coin that Zoey and Gabe use is a regular coin, Zoey is positive that the tradition is unfair. The coin lands on heads way more often than tails, and Zoey has to take out the trash more. Zoey believes that the coin is statistically more likely to land on heads. What do you think?

In order to understand Zoey's problem, we need to understand binomial experiments. In this lesson, you will learn about binomial experiments and how to identify them.

## Understanding Binomial Experiments

Before we talk more about Zoey's problem, let's talk about an experiment Gabe and his friends are conducting. Gabe and his friends are hanging out at the local arcade. His friends dare him to ask 20 girls for their phone numbers. The friends watch as Gabe has some trouble getting phone numbers from girls at the arcade. Gabe asks the twelfth girl for her number. He hasn't gotten any so far, so they bet that Gabe will be unsuccessful with this girl. Gabe and his friends are conducting a binomial experiment, which is an experiment that contains a fixed number of trials that results in only one of two outcomes: success or failure.

There are some things to keep in mind when understanding binomial experiments. First, the outcomes must be independent. This means that the outcome of one trial cannot have any influence on another. With Gabe's experiment, we have to assume that when Gabe asks one girl for her phone number, her response does not influence the outcome of any other girl. If Gabe asks one girl for her phone number and she says no, and Gabe then asks her nearby friend who also says no, then it's possible that the first girl's response influenced the second girl's response. Only when the outcomes are independent can the experiment be considered binomial.

Second, a binomial experiment must only have two possible outcomes. In the case of Gabe's experiment, he can only receive yes or no answers. If the girls answered 'maybe' or 'later', then this would not be considered a binomial experiment.

Third, there are a fixed number of trials. Gabe and his friends said he would only ask 20 girls. If the bet, or experiment, was to ask as many girls as he could until he got a number, then this would not be a binomial experiment. Let's practice identifying them.

## Identifying Binomial Experiments

Let's go back to Zoey's issue with taking out the trash based on the flip of a coin. She asks Gabe if they can conduct an experiment. She wants to see how many times heads will come up if they flip the coin ten times. Is this a binomial experiment? Are the outcomes independent? Are there only two possible outcomes? Is there a fixed number of trials?

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