Back To Course

Statistics 101: Principles of Statistics11 chapters | 144 lessons | 9 flashcard sets

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

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.

Probability can get very confusing at times. You will find that some words, such as events and subsets, are often referring to the same concept depending on the experiment. Use this lesson to understand the concept of events as subsets.

Bianca, Megan and Nick are sitting at their favorite Italian restaurant. It's lunchtime, so the waiter hands them each a lunch menu. The menu is comprised of four different items: lasagna, spaghetti, fettuccine Alfredo or pizza. They can also order a sampler, which is a small portion of each of the items on the menu. There are a lot of different combinations that these friends can have as a meal. In statistics, you will find experiments that have many possible outcomes and combinations. What do we call these experiments and outcomes? Some terms that you will come across are subsets, events and sample spaces.

When you conduct an experiment, you are observing certain outcomes. For example, you may be conducting an experiment on flipping a coin. The possible outcomes for flipping a coin are heads or tails. If you were rolling a six-sided die, then the possible outcomes would be 1, 2, 3, 4, 5 or 6. There are no other possible outcomes. We call these possible outcomes **sample spaces**. A sample space is a set (S) of a random experiment that includes all possible outcomes of the experiment.

In our opening scenario, one of the options on the menu was a sampler. Let's say that the sampler is a small portion of everything else that's on the menu. You can think about sample spaces as the sampler on a menu; it gives you an idea or picture of all of the possible outcomes in the experiment. For example, if Megan ordered the sampler, she knows she's not going to get tacos as part of her meal. Tacos are not part of the sample space in this case.

Now that we know about sample space, what about the actual results of the experiment? You will hear two words in statistics: events and subsets. Before we define these things, you must remember something very important: events are subsets, and subsets are events. An **event** is a possible outcome of an experiment. And a **subset** is an event of a sample space. Therefore, if Bianca ordered a pizza, that would be an event, or subset, of the sample space.

When you think of subsets, think of what that word means. Look at the prefix 'sub-'. Think of the words you know that include 'sub-' as a prefix: subway, submarine, subordinate, subheading. In this case, sub- means below or beneath. A subheading for an essay is something that is beneath and part of the main heading. Think of the subset as being beneath, or a part of, the sample space.

Let's go back to our rolling the dice scenario. If you were to roll one die, your sample space would be 1, 2, 3, 4, 5 or 6. A subset of this sample space might be 1 because you can roll a die and get a 1. You cannot roll a die and get a 7. Therefore, 7 is not a subset of the sample space.

Bianca, Megan and Nick are sitting at their favorite Italian restaurant. It's lunchtime, so the waiter hands them each a lunch menu. The menu is comprised of four different items: lasagna, spaghetti, fettuccine Alfredo or pizza. They can also order a sampler, which is a small portion of each of the items on the menu. In this scenario, the sampler represents our sample space, because it represents all of the possible options on the menu. Bianca orders a pizza, Megan orders the lasagna and Nick orders the spaghetti. Therefore, the subsets for this experiment are lasagna, spaghetti and pizza. All of these items are on the menu and part of the sample space.

Sometimes describing events as subsets of a sample space can get a bit confusing. Remember, events are subsets, and subsets are events. An **event** is a possible outcome of an experiment, and a **subset** is an event of a sample space. A **sample space** is a set (S) of a random experiment that includes all possible outcomes of the experiment. To help remember the differences in these concepts, remember the Italian restaurant menu. A sample space is all of the possible outcomes, which are all of the things that appear on the menu. A subset is an event in the experiment, so any items on that menu could be considered a subset depending on what the person orders!

You'll have the ability to do the following after this lesson:

- Define event, subset and sample space
- Explain how to remember the differences between events and subsets

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
2 in chapter 4 of the course:

Back To Course

Statistics 101: Principles of Statistics11 chapters | 144 lessons | 9 flashcard sets

- Mathematical Sets: Elements, Intersections & Unions 3:02
- Events as Subsets of a Sample Space: Definition & Example 4:51
- Probability of Independent and Dependent Events 12:06
- Probability of Independent Events: The 'At Least One' Rule 5:27
- How to Calculate Simple Conditional Probabilities 5:10
- The Relationship Between Conditional Probabilities & Independence 7:52
- Using Two-Way Tables to Evaluate Independence 8:09
- Applying Conditional Probability & Independence to Real Life Situations 12:32
- The Addition Rule of Probability: Definition & Examples 10:57
- The Multiplication Rule of Probability: Definition & Examples 8:37
- Math Combinations: Formula and Example Problems 7:14
- How to Calculate a Permutation 6:58
- How to Calculate the Probability of Permutations 10:06
- Relative Frequency & Classical Approaches to Probability 5:56
- Go to Probability

- Go to Sampling

- Computer Science 335: Mobile Forensics
- Electricity, Physics & Engineering Lesson Plans
- Teaching Economics Lesson Plans
- U.S. Politics & Civics Lesson Plans
- US History - Civil War: Lesson Plans & Resources
- HESI Admission Assessment Exam: Factors & Multiples
- HESI Admission Assessment Exam: Probability, Ratios & Proportions
- HESI Admission Assessment Exam: 3D Shapes
- HESI Admission Assessment Exam: Punctuation
- HESI Admission Assessment Exam: Linear Equations, Inequalities & Functions
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison
- TACHS Prep Product Comparison
- Top 50 Blended Learning High Schools
- EPPP Prep Product Comparison

- History of Sparta
- Realistic vs Optimistic Thinking
- How Language Reflects Culture & Affects Meaning
- Logical Thinking & Reasoning Questions: Lesson for Kids
- Exceptions to the Octet Rule in Chemistry
- Database Hacking: Attack Types & Defenses
- Pride and Prejudice Discussion Questions
- Quiz & Worksheet - Frontalis Muscle
- Quiz & Worksheet - Dolphin Mating & Reproduction
- Octopus Diet: Quiz & Worksheet for Kids
- Quiz & Worksheet - Fezziwig in A Christmas Carol
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- What is Cooperative Learning? | Cooperative Learning Guide for Teachers
- Pronoun Worksheets

- Instructional Strategies for Teaching History
- Common Core ELA Grade 7 - Writing: Standards
- Intro to Algebra
- Accuplacer ESL Reading Skills Test: Practice & Study Guide
- High School Geometry Textbook
- Reading Essays - Basics: AP English Language Lesson Plans
- Social Cognition & Perception in Social Psychology Lesson Plans
- Quiz & Worksheet - Polar Bear Food Chain
- Quiz & Worksheet - Zygote
- Quiz & Worksheet - Unearned Revenue
- Quiz & Worksheet - Calculating Asset Turnover Ratios
- Quiz & Worksheet - The Copper Age

- Philip II of Spain: Accomplishments & Biography
- Chromatid: Definition & Exchange
- Alternative Teacher Certification in Maryland
- Math Riddles for Kids
- 100th Day of School Project Ideas
- High School Math Games
- Homeschooling in Idaho
- Poetry Activities for Kids
- Social Studies Games for Kids
- Oregon Science Standards for 5th Grade
- Common Core Standards in Rhode Island (RI)
- Writing Center Resources

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject