NZ Level 4
Sample Spaces
Lesson

In probability, the sample space is a list of all the possible outcomes of an experiment.

Outcomes are the results of an experiment. For example, think about flipping a coin. There are two possible outcomes - a head or a tail. So when we list (or write out) the sample space, we'd write:

{$\text{heads, tails}$heads, tails}

There are some common items used in probability questions, including cards, dice, coins so it's good to be familiar with their characteristics.

Handy Facts
• There are $52$52 cards in a standard deck.
• A standard die has $6$6 faces (because it's a cube)
• A coin has $2$2 faces- heads and tails

#### Examples

##### Question 1

A jar is filled with $4$4 blue marbles and $3$3 red marbles and one is to be chosen at random. List the sample space.

Think: What are all the possible options for what marble will be selected?

Do: {$\text{blue, red}$blue, red}

##### Question 2

The spinner below is spun.

List the sample space.

Think: What are all the possible outcomes?

Do: {$\text{yellow, green, red, blue}$yellow, green, red, blue}

##### Question 3

A standard six-sided die is rolled.

1. List the sample space.

(Separate outcomes with a comma)

2. List the sample space for rolling a number strictly less than $3$3. Separate outcomes with a comma.

3. List the sample space for rolling a number divisible by $3$3. Separate outcomes with a comma.

4. List the sample space for rolling an even number. Separate outcomes with a comma.

### Outcomes

#### S4-3

Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence