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In mathematics, sample space is the set of all possible outcomes of an experiment or situation. In mathematics, sample space is the set of all possible outcomes of an experiment or situation. An outcome is a result of an experiment. For instance, if we were flipping a coin, there are only two possible outcomes (sample space) which are heads or tails. If we were to roll a six-sided die, the sample space would be six possible values. Sample space is normally signified by the letter "S", which make sense. You may also see it signified by the use of brackets { }. All of the values that reside within those brackets are the data points we are expecting. Being able to understand all the possibilities of an experiment help us to better understand the odds of achieving those results. As we cruise through all of the work on this page, we will explain how to breakdown a scenario and understand the chance end results.

In these worksheets, students will work with sample spaces. In these worksheets, students will learn how to determine sample spaces. They will find sample spaces for given situations. All problems are presented as word problems, describing a specific situation. This set of worksheets contains step-by-step solutions to sample problems, both simple and more complex problems, a review, and a quiz. It also includes ample worksheets for students to practice independently. Additional paper may be required in order for students to have room for their calculations. Worksheets are provided at both the basic and intermediate skills levels. When finished with this set of worksheets, students will be able to find sample spaces for situations. These worksheets explain how to determine sample spaces. Sample problems are solved and practice problems are provided.

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Sample Spaces Worksheets

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Introduction to Sample Spaces Lesson

This worksheet explains how to determine the number of possible outcomes. A practice problem is solved, and two practice problems are provided.

Worksheet

Example: A student can select one of 6 different Chemistry, one of 6 different Biology books and one of 5 different science books. List the sample spaces.

Practice

Problem example: A magician ask one of the people in the audience to roll 4 dice and draw two cards from a bag numbered 1 to 5 simultaneously. List the sample spaces for both.

Review

You will work on some unique scenarios like: Determine the possible number of outcomes of herbs if there are 2 species available in 4 heights and 7 different quality levels?

Quiz

Students will demonstrate their proficiency with this types of problems. Ten problems are provided.

Check

A menu has 4 different sandwiches and 2 drinks. How many different ways could you place an order, if you always had one drink and sandwich?

Sample Spaces Worksheet

. A magician asks someone in the audience to roll 4 dice and draw two cards from a bag numbered 1 to 5 simultaneously. How many different ways could you arrange this situation?

Practice

Students will practice finding the sample spaces for each situation. Ten problems are provided.

Review

The concept we have explored are worked out for each situation. A sample problem is solved and six practice problems are provided.

Quiz

Students will demonstrate their proficiency with this skill. Ten problems are provided.

Check

A great way to practice this skill in a friendly manner. Three problems are provided, and space is included for students to copy the correct answer when given.

Basic Skills Worksheet

Example: What is the probability that a card randomly selected from a standard deck will be an ace and a club?

Basic Skills Practice

Example: Find the odds of randomly choosing the letter A from a bag that contains the letters in the name of TWELVE.

Sample Spaces Intermediate Skills Worksheet

Students will use intermediate skills to find the solution to exercises that matches this topic well. Ten problems are provided.

Intermediate Skills Practice

Example: A large basket of fruit contains 5 oranges, 8 apples and 7 bananas. If a piece of fruit is chosen at random, what is the probability of getting an orange or a banana?

Intermediate Skills Drill

SApply what you have learned to solve problems like: Our alphabet contains 26 letters. Five of these letters are vowels (A, E, I, O, U). The remaining 21 letters are called consonants. Each letter of the alphabet is written on a card and you are asked to choose a card. What is the probability of choosing vowels?

Example Sample Space Problems

Practice#1: What is the probability of a single result when you toss a coin? Results: The results of this practice are the head and tail. Probabilities: P(head) = ½ , P(tail) = ½ . Definition: The sample space of practice is the collection of all probable results of that practice. It is denoted by the symbol {S}. {S} (practice#1) = (head and tail). Practice#2: A glass jar contains red(1), green(3), blue(2), and yellow(4) marbles. If we pick one from the jar, what will be the probability of each result? {S}: (Red), (Yellow), (Blue), (Green) Probabilities(P): P(R) = 1/10, P(G) = 3/10, P(B)= 2/10 = 1/5, P(Y) = 4/10 = 2/5. Above practices#1&2 shows the total probabilities of a single result =1. It is because the sum of the probabilities of the separate results within a {S} = 1. Practice#3: The {S} for picking only one card at chance from a deck of 52 playing cards. There are 52 probable results in {S}. The probability of each result of this practice is: P(card) = 1/52. The total of the probabilities of individual results within this {S} will be: 52 / 52 =1.