Sample space for children

Quick answer

A sample space is simply a list of all the possible outcomes in a situation. For example, if you flip a coin, the sample space is heads or tails.

Learning outcome

By the end of this page, you will be able to list all the possible results in a simple situation, like rolling a dice or picking a colour from a bag.

Success signs:

• You can name all the possible outcomes in a simple event
• You can draw or write a list of all results
• You can explain why some outcomes are not possible
• You can use sample space to help you predict what might happen

Why this matters

Knowing all the possible results helps you understand how likely something is to happen. It’s like having a map of all the paths you could take. In games, sports, and even daily life, sample spaces help us make smart choices. For example, if you know all the possible outcomes when rolling a dice, you can plan your next move in a board game.

How it works

Sample space is a way to list all the things that can happen in a situation. Here’s how to find it:

1. Think about what can happen in the situation
2. Write down each possible result
3. Make sure you don’t miss any
4. Check if any results are the same or can’t happen

For example, if you roll a dice, the possible results are 1, 2, 3, 4, 5, or 6. These are all the numbers on the dice, so that’s your sample space.

Examples you can see

Let’s look at some simple examples of sample spaces:

Example 1: Flipping a coin

When you flip a coin, it can land on either heads or tails.

Sample space = {heads, tails}

Example 2: Rolling a dice

A dice has six sides, numbered 1 to 6.

Sample space = {1, 2, 3, 4, 5, 6}

Example 3: Picking a colour from a bag

If a bag has 3 red marbles, 2 blue marbles, and 1 green marble, you can pick one of these colours:

Sample space = {red, blue, green}

Example 4: Choosing a day of the week

There are 7 days in a week:

Sample space = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

Example 5: Playing rock, paper, scissors

In this game, you can choose one of three things:

Sample space = {rock, paper, scissors}

Try it as a mini adventure

Imagine you are a detective solving a mystery. You need to find all the possible suspects in a story. Here’s your challenge:

1. There are 4 people who could have been at the scene: Alex, Bella, Charlie, and Daisy.
2. Each person could have done one of three things: stolen a key, broken a window, or drawn a sketch.

Your mission: List all the possible outcomes for one person doing one action.

First, list all the actions:

• Stole a key
• Broke a window
• Drew a sketch

Then, list all the people:

• Alex
• Bella
• Charlie
• Daisy

Now, combine them to find all the possible outcomes:

• Alex stole a key
• Alex broke a window
• Alex drew a sketch
• Bella stole a key
• Bella broke a window
• Bella drew a sketch
• Charlie stole a key
• Charlie broke a window
• Charlie drew a sketch
• Daisy stole a key
• Daisy broke a window
• Daisy drew a sketch

There are 12 possible outcomes in this case. You’ve found the sample space!

Common mistakes

• Mistake: Forgetting to list all possible outcomes
• Why it happens: When we are excited or in a hurry, we might miss one or two things.
• Fix: Take your time and think through each possibility. Use a list or draw a table to help you.

• Mistake: Writing the same outcome twice
• Why it happens: Sometimes we accidentally write the same thing more than once.
• Fix: Check your list and cross off items as you go to make sure you don’t repeat them.

• Mistake: Including impossible outcomes
• Why it happens: Sometimes we include things that can’t happen, like a dice showing 7 or 8.
• Fix: Think carefully about what is possible in the situation. If a dice only has 1 to 6, then 7 or 8 are not part of the sample space.

Parent and carer guide

Help your child understand sample spaces by:

• Using everyday situations like choosing a snack or picking a card from a deck
• Encouraging them to write or draw their sample spaces
• Asking them to explain their thinking
• Practising with simple examples like flipping a coin or rolling a dice
• Not worrying if they miss a few at first – it’s a skill that gets better with practice

Tip: Use a chart or table to help your child see all the possibilities clearly. For example, when rolling a dice, you can make a list of numbers 1 to 6. When choosing from a bag, you can draw the items or write their names.

Practice questions

1. What is the sample space for flipping a coin?
2. What is the sample space for rolling a dice?
3. What is the sample space for choosing a colour from a bag that has 3 red, 2 blue, and 1 yellow marble?
4. What is the sample space for picking a day of the week?
5. What is the sample space for playing rock, paper, scissors?

Answers:

1. {heads, tails}
2. {1, 2, 3, 4, 5, 6}
3. {red, blue, yellow}
4. {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
5. {rock, paper, scissors}

FAQ

What is a sample space?

A sample space is a list of all possible outcomes in a situation. For example, when flipping a coin, the sample space is heads or tails.

Why do we need sample spaces?

Sample spaces help us understand all the possible results in a situation. This helps us make predictions and decisions.

Can sample spaces be more than two outcomes?

Yes! Sample spaces can have many outcomes. For example, rolling a dice has 6 possible outcomes, and choosing a day of the week has 7.

Can a sample space include impossible outcomes?

No. A sample space only includes outcomes that can actually happen. For example, a dice can’t show 7 or 8, so those are not part of the sample space.

How can I help my child learn about sample spaces?

You can use games, real-life examples, and drawing or writing out outcomes to help your child understand. Practice with simple situations like flipping a coin or choosing a colour from a bag.