Solving Problems with Binomial Experiments: Steps & Example

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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.

Sometimes when conducting research you will need to use binomial experiments to solve problems. In this lesson, you will learn about binomial experiments and how to use probability to solve problems.

Understanding Binomial Experiments

Jeanette is working on a project for her technology class. Her teacher wants to know the answers to the following questions:

1. What is the probability that a student enrolled in a technology class is already comfortable using technology?
2. What is the probability that a student enrolled in a history class is comfortable using technology?
3. What is the probability that a student enrolled in a math class is comfortable using technology?

The teacher asks the students to do three things:

1. Make a hypothesis of the probability of each question
2. Calculate the theoretical probability
3. Calculate the actual probability

This problem can be solved using 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. In this lesson, you will learn how to answer Jeanette's homework questions using binomial experiments and probability.

There are some things to keep in mind when undertaking binomial experiments. First, the outcomes must be independent. This means that the outcome of one trial cannot have any influence on another. For example, when Jeanette asks the students if they are comfortable with technology, she will need to ask them individually. If she asks them in groups, one person's response might influence how the others will respond.

Second, a binomial experiment must only have two possible outcomes. For example, Jeanette surveys the students in her class, asking them if they are comfortable working with technology. She asks them to answer this question 'yes' or 'no'. In this case, there are only two possible outcomes for the response: yes or no.

Third, there are a fixed number of trials. For example, Jeanette decides to ask 20 people in each class: technology, history, and math. Therefore, she has a fixed number of people she will be asking.

Now that you understand binomial experiments. Let's try to solve Jeanette's probability problems. If you need more details on binomial experiments, check out our other lessons!

Binomial Experiment Problems

Remember, Jeanette's teacher asked her to determine the following:

1. Make a hypothesis of the probability of each question
2. Calculate the theoretical probability
3. Calculate the actual probability

Let's focus on the technology class. Before asking her classmates if they are comfortable using technology, Jeanette guesses that 80% of the technology students are comfortable using the technology. She chooses this high number because she believes the students would not be in a technology class unless they enjoy using technology.

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