term	definition
Experiment	A repeatable process.
Event	One or more possible outcomes of an experiment.
Sample space	The set of all possible outcomes of an experiment.

Representing sample space

The sample space of an experiment can be represented with a sample space diagram. These are an easy way to list possible outcomes.

Example 1

A fair coin is tossed $3$ times. What is the sample space of this experiment?

Let $H$ represent heads, and $T$ represent tails.

The set of possible options is:

$\underline{\{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\}}$

Example 2

Two fair dice are tossed, and the numbers that they land on are multiplied together. What is the probability that the two numbers multiply to give $12$ ?

Draw a table to represent the sample space:

	die 1
die 2	$\bf \times$	$\bf1$	$\bf2$	$\bf3$	$\bf4$	$\bf5$	$\bf6$
	$\bf1$	$1$	$2$	$3$	$4$	$5$	$6$
	$\bf2$	$2$	$4$	$6$	$8$	$10$	$12$
	$\bf3$	$3$	$6$	$9$	$12$	$15$	$18$
	$\bf4$	$4$	$8$	$12$	$16$	$20$	$24$
	$\bf5$	$5$	$10$	$15$	$20$	$25$	$30$
	$\bf6$	$6$	$12$	$18$	$24$	$30$	$36$

Identify the desired events in the sample space:

	die 1
die 2	$\bf \times$	$\bf1$	$\bf2$	$\bf3$	$\bf4$	$\bf5$	$\bf6$
	$\bf1$	$1$	$2$	$3$	$4$	$5$	$6$
	$\bf2$	$2$	$4$	$6$	$8$	$10$	$\large\textcircled{\small12}$
	$\bf3$	$3$	$6$	$9$	$\large\textcircled{\small12}$	$15$	$18$
	$\bf4$	$4$	$8$	$\large\textcircled{\small12}$	$16$	$20$	$24$
	$\bf5$	$5$	$10$	$15$	$20$	$25$	$30$
	$\bf6$	$6$	$\large\textcircled{\small12}$	$18$	$24$	$30$	$36$

Calculate the probability:

$4$ outcomes out of $6\times6=36$ options.

The probability that the two numbers multiply to give $12$ is $\dfrac{4}{36}=\underline{\dfrac{1}{9}}$ .

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FAQs - Frequently Asked Questions

How do you represent sample space?

Sample space can be represented with either a set or a sample space diagram.

What is an experiment?

An experiment is a repeatable process.

What is a sample space?

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

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Representing sample space

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die 1

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die 1

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