To list the outcomes of an experiment, we first need to examine the experiment completely to identify all the possible outcomes. We can illustrate this with the following examples.

Example $1$

Consider an experiment where we want to know what number we land on when rolling a six-sided die.

To list all of the possible outcomes, we need to think about every single option that could be the result of the experiment. When rolling the die, it can land on any number from

1

to

6 .

Therefore, the sample space includes the set of integers from

1

to

6 .

We can list these outcomes as a set.

{1, 2, 3, 4, 5, 6}

Usually, when listing possible outcomes, we want to add some kind of additional information. Suppose we roll the die

10

times and are interested in knowing the outcomes for each roll. We can write this by listing the outcomes in a table.

Outcome	Tally
$1$	$2$
$2$	$1$
$3$	$3$
$4$	$0$
$5$	$3$
$6$	$1$

Example $2$

Now consider an experiment where we are drawing a card from a standard deck and we want to know its suit.

Even though there are many kinds of cards for each suit, the only outcomes we care about right now are the suits themselves. Therefore, the sample space consists of the four suits: Clubs, Diamonds, Spades, and Hearts. We can list the sample space in a set.

{Clubs, Diamonds, Spades, Hearts}

Suppose we draw

10

cards from the deck. Let's write the outcomes in a table.

Suits	Tally
Clubs	$2$
Diamonds	$4$
Spades	$3$
Hearts	$1$

Example 1

Example 2

Example $1$

Example $2$

Exercise