Formula of Sample Space in Math

Lesson Transcript
Meredith Fontana
Expert Contributor
Christianlly Cena

Christianlly has taught college Physics, Natural science, Earth science, and facilitated laboratory courses. He has a master's degree in Physics and is currently pursuing his doctorate degree.

Sample space refers to all potential outcomes from a study, often estimated before experimenting. Identify the method used to determine sample space through two example problems, including the calculations of probability. Updated: 01/04/2022

What Is Sample Space?

Life is a game of chance and choice. We live in a day and age where choices bombard us on things that weren't available to us years ago. And because of this reality, the concept of probability and sample space have become a part of our lives even if we aren't always aware of it. Take for instance, cell phones. Today there are hundreds of different phones available for consumers to purchase. What if we wanted to find out how many different cell phones are available for purchase or lease? The number of cell phones available can be seen as the sample space of an experiment or study involving cell phones. Sample space is the number of possible outcomes of an experiment or study.

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Measures of Variability: Range, Variance & Standard Deviation

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:04 What Is Sample Space?
  • 0:44 Finding Sample Space
  • 2:16 Probability & Specific Events
  • 4:01 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed

Finding Sample Space

Unlike many math concepts, there isn't a specific formula for how to find sample space, unless you are given other related values that we will discuss later. What do we mean by this? Well, let's look at a few examples to show you what we mean.

Example 1

What is the sample space of rolling a six-sided die?

The sample space would be the possible outcomes from rolling the dice {1, 2, 3, 4, 5, 6}. In other words, there are six possible outcomes for this problem.

Example 2

What is the sample space of picking a consonant from the alphabet if each letter is written on an individual piece of paper?

The sample space would be the possible outcomes from picking a piece of paper with a consonant written on it: {B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z}. In other words, there are 21 possible outcomes for selecting a piece of paper with a consonant on it.

Notice in both of our examples, that a mathematical formula wasn't used to derive our answer. We had to obtain our answer based on information given in the problem. When no other related pieces of information are given other than what is being studied, we must carefully read the problem to come up with our correct sample space. A deck of cards, the numbers on a pair of dice, and the sides of a coin are examples of cases where we can easily figure out the sample size.

To unlock this lesson you must be a Member.
Create your account

Additional Activities

Formula of Sample Space in Math: Practice Problems

In this activity, you will check your knowledge of how to find sample space for experiments, studies, or specific events.


For this activity, print or copy this page on a blank piece of paper. Then, carefully read the given word problems and provide a solution.

1.) In a business study conducted for an up-and-coming cereal brand, it was found out that the probability of people buying Cheerios is 3/5 and that the number of people who buy Cheerios is sixty. Find the sample space of possible outcomes on the study on cereal brands.

2.) A school conducts a study on milk brands that students prefer to include in school meals. They found out that the probability of students preferring brand ZY milk is 2/3 and that the number of students who actually prefer the said brand is eighty-two. Find the sample space of possible outcomes on milk brands.

Answer Key

Use the formula P = Specific Event / Sample Space to find the sample space.

Use the variable S to represent sample space.

1.) plug P = 3/5, SE = 60

3/5 = 60 / S

Cross multiply

There are 100 possible outcomes on this study on cereal brands.

2.) plug P = 2/3 , SE = 82

2/3 = 82 / S

Cross multiply

There are 123 possible outcomes on this study on milk brands.

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back

Resources created by teachers for teachers

Over 30,000 video lessons & teaching resources‐all in one place.
Video lessons
Quizzes & Worksheets
Classroom Integration
Lesson Plans

I would definitely recommend to my colleagues. It’s like a teacher waved a magic wand and did the work for me. I feel like it’s a lifeline.

Jennifer B.
Jennifer B.
Create an account to start this course today
Used by over 30 million students worldwide
Create an account