How do you create a sample space?

The following diagram shows how the sample space for an experiment can be represented by a list, a table, and a tree diagram. Scroll down the page for examples and solutions.

In the study of probability, an experiment is a process or investigation from which results are observed or recorded.

An outcome is a possible result of an experiment.

A sample space is the set of all possible outcomes in the experiment. It is usually denoted by the letter S. Sample space can be written using the set notation, { }.

Experiment 1: Tossing a coin
Possible outcomes are head or tail.
Sample space, S = {head, tail}

Experiment 2: Tossing a die
Possible outcomes are the numbers 1, 2, 3, 4, 5, and 6
Sample space, S = {1, 2, 3, 4, 5, 6}

Experiment 3: Picking a card
In an experiment, a card is picked from a stack of six cards, which spell the word PASCAL.
Possible outcomes are P, A 1, S, C, A 2 and L.
Sample space, S = {P, A 1, S, C, A 2 L}. There are 2 cards with the letter ‘A’

Experiment 4: Picking 2 marbles, one at a time, from a bag that contains many blue and red marbles.
Possible outcomes are: (Blue, Blue), (Blue, Red), (Red, Blue) and (Red, Red).
Sample space, S = {(B,B), (B,R), (R,B), (R,R)}.

A simple explanation of Sample Spaces for Probability

Sample Space Of An Event

Sample space is all the possible outcomes of an event. Sometimes the sample space is easy to determine. For example, if you roll a dice, 6 things could happen. You could roll a 1, 2, 3, 4, 5, or 6.

Sometimes sample space is more difficult to determine, so you can make a tree diagram or a list to help you figure out all the possible outcomes.

Example 1:
You are ordering pizza. You can choose a small, medium or large pizza and you can choose cheese or pepperoni. What are the possible ways that you could could order a pizza? How many combinations could you have?

Example 2:
Daisy has 3 pairs of shorts, 2 pairs of shoes and 5 t-shirts. How many outfits can she make?

This lesson is on finding simple probabilities and sample spaces.

Example:
When you roll a die,

1. what is the sample space?
2. P(5)
3. P(Even)
4. P(Prime)
5. P(7)

Example:
Use the spinner below to answer the following questions:

1. What is the sample space?
2. P(Blue)
3. P(Orange or Green)
4. P(Not Red)
5. P(Purple)

The following video explains simple probability, experiments, outcomes, sample space and probability of an event. It also gives an example of a simple probability problem.

Example:
A jar contains five balls that are numbered 1 to 5. Also, two of the balls are yellow and the others are red. They are numbered and colored as shown below.

1. Find the probability of randomly selecting a red ball.
2. Find the probability of randomly selecting an even number ball.

Lists and Sample Spaces - Probability

Example:
Entrees - Ribs, Chicken
Sides - Mac and Cheese, Veggies, Mashed Potatoes
Drinks - Water, Coffee, Milk
What are the different possibilities for the menu?

Explains three methods for listing the sample space of an event and introduces conditional probability: List, Table, Tree Diagram.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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What is Sample Space and How to Find Sample Space

Definition: The sample space of an experiment is the set of all possible outcomes of that experiment.

Experiment 1: What is the probability of each outcome when a dime is tossed?

Outcomes: The outcomes of this experiment are head and tail.

Probabilities: 

P(head) = 12 P(tail) = 12

The sample space of Experiment 1 is:   {head, tail}

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Experiment 2: A spinner has 4 equal sectors colored yellow, blue, green and red. What is the probability of landing on each color after spinning this spinner?

  

Sample Space: {yellow, blue, green, red}

Probabilities:

P(yellow) = 14 P(blue) = 14 P(green) = 14 P(red) = 14

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Experiment 3: What is the probability of each outcome when a single 6-sided die is rolled?

  

Sample Space: {1, 2, 3, 4, 5, 6}

Probabilities: 

P(1) = 16 P(2) = 16 P(3) = 16 P(4) = 16 P(5) = 16 P(6) = 16

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Experiment 4: A glass jar contains 1 red, 3 green, 2 blue and 4 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of each outcome?

Sample Space: {red, green, blue, yellow}

Probabilities: 

P(red) =  1 10 P(green) =  3 10 P(blue) =  2  = 1105 P(yellow) =  4  = 2105

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Summary: The sample space of an experiment is the set of all possible outcomes for that experiment. You may have noticed that for each of the experiments above, the sum of the probabilities of each outcome is 1. This is no coincidence. The sum of the probabilities of the distinct outcomes within a sample space is 1.

The sample space for choosing a single card at random from a deck of 52 playing cards is shown below. There are 52 possible outcomes in this sample space.

The probability of each outcome of this experiment is:

P(card) =  1 52

The sum of the probabilities of the distinct outcomes within this sample space is:

52 = 152

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Exercises

Directions: Read each question below. Select your answer by clicking on its button. Feedback to your answer is provided in the RESULTS BOX. If you make a mistake, choose a different button.

What is the formula for sample space?

The sample space is S = {H, T}. E = {H} is an event. Example 2 Tossing a die. The sample space is S = {1,2,3,4,5,6}.

What is sample space with example?

Sample Space- Examples When we toss a coin, there can be only two outcomes i.e., either head or tail. So, the sample space will be, S = {H, T} where H is the head and T is the tail. With this, we know that if we have 'n' coins, the possible number of outcomes will be 2n.

What is sample space of an experiment?

The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment. In a random experiment, the outcomes, also known as sample points, are mutually exclusive (i.e., they cannot occur simultaneously).

What is a sample space in math?

Informally, the sample space for a given set of events is the set of all possible values the events may assume. Formally, the set of possible events for a given random variate forms a sigma-algebra, and sample space is defined as the largest set in the sigma-algebra.