# Sample Spaces Worksheets

What Are Statistical Sample Spaces? In statistics, we define sample space as the set of all the possible results of an experiment. The number of outcomes or results present in a sample space depends on the random experiment. In case a sample space has a finite or set number of outcomes, then that sample space is known as finite or discrete. In sample space, events are defined as the subset of all the likely outcomes. We represent sample space by using a symbol 'S'. We enclose a sample space of a random experiment with a curly bracket {}. Most people often confuse sample space and the possible outcomes when we write sample space of any given experiment we write {1, 2, 3, 4, 5, 6}. However, when we are to write the possible outcomes, it can be written as a set of odd outcomes {1, 3, 5}, or even outcomes {2, 4, 6}. Outcomes can be random, but sample space is the universal set for a particular experiment. If we consider an experiment of the coin toss, we will get only two possible outcomes, that is head and tail. Hence, the sample space of a coin toss will be written as: Sample Space (S) = {Head, Tail} or {H, T}. However, the set is different when we flip two coins. Let H1 and T1 be the outcomes of the first coin, and H2 and T2 be the outcomes of the second coin. The possible outcomes can be written as: Sample Space (S) = {(H1, H2), (H1, T2), (T1, H2), (T1, T2)}.

• ### Basic Lesson

Introduces the concept of determining the number of elements involved in a problem. How many elements are in the sample space of tossing one coin? List the sample space. A sample space is a set of all possible outcomes for an activity or experiment. A coin has only two possibilities that are either heads or tails. So there will be 2 outcomes in the sample space: {Heads, Tails}

• ### Intermediate Lesson

This lesson focuses on listing the sample spaces. You draw one ball from a hat which has red, green, blue and white balls. List the sample space. There are four possibilities to select one ball from hat. So there will be 4 outcomes in the sample space: {red ball, green ball, blue ball, or white ball}

• ### Independent Practice 1

Students practice with 20 Sample Spaces problems. The answers can be found below. There are 3 entry doors and 3 staircases in a building. List the sample space of using an entry door and one staircase.

• ### Independent Practice 2

Another 20 Sample Spaces problems. The answers can be found below. A model of computer comes with 3 different processor speeds and 6 different memory sizes.

• ### Homework Worksheet

Reviews all skills in the unit. A great take home sheet. Also provides a practice problem. Choosing an outfit from a blue shirt, a white shirt, a black pant, a pair of black shoes, and a pair of brown shoes?

• ### Skill Quiz

10 problems that test Sample Spaces skills.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

Answers for the lesson and practice sheets.

• ### Basic Lesson

Introduces the fundamentals of Sample Spaces. Provides a basic application.

• ### Intermediate Lesson

This lesson focuses on determining the outcome of Sample Spaces with word problems.

• ### Independent Practice 1

Students practice with 20 Sample Spaces problems. The answers can be found below. How many possible combinations are there from 8 pizza flavors and 4 different sizes?

• ### Independent Practice 2

Another 20 Sample Spaces problems. The answers can be found below. A student can select one of 5 different history books, one of 6 different math books and one of 3 different science books.

• ### Homework Worksheet

Reviews all skills in the unit. A great take home sheet. Also provides a practice problem.

• ### Skill Quiz

10 problems that test Sample Spaces skills.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.