Wizard school maths quest: probability

Quick answer

Probability is about how likely something is to happen – from certain to impossible – and we can use words like "likely", "unlikely", "certain", and "impossible" to describe it.

Learning outcome

By the end of this page, you will be able to describe how likely events are using words like impossible, certain, likely, and unlikely, and understand that the more chances something has, the more likely it is to happen.

Success signs:

• You can sort events from impossible to certain
• You can explain why some events are more likely than others
• You can use probability words in everyday situations
• You can predict what might happen in a simple game or experiment

Why this matters

Probability helps us understand what might happen in the future. It’s useful in many parts of life – from deciding whether to take an umbrella when it's cloudy, to choosing which game to play, or even helping wizards know which spell might work best! When you understand probability, you can make better choices and think more carefully about what might happen.

How it works

Probability is about how much chance there is that something will happen. We can describe this chance using words:

1. Certain – Something that will definitely happen (like the sun rising tomorrow)
2. Impossible – Something that will never happen (like a human flying without wings)
3. Likely – Something that probably will happen (like getting a head when flipping a coin)
4. Unlikely – Something that probably won’t happen (like finding a gold coin in your pocket)

We can also use a number line to show how likely things are – from 0 (impossible) to 1 (certain).

Examples you can see

Let’s imagine you're at a wizard school, and you're learning about probability by making potions and casting spells.

Example 1: The Potions Room

In the potions room, you mix ingredients to make a spell. You know that:

• Water is always in a potion – so it’s certain you’ll find water
• Only one of the potions will make a dragon appear – so that’s unlikely to happen
• If you mix the wrong ingredients, the potion might explode – so that’s possible but unlikely
• It's impossible to make a potion that makes a unicorn appear if there are no unicorn horns in the room

Example 2: Spell Casting

You're casting a spell and roll a dice to see if it works:

• Rolling a number between 1 and 6 is certain (you’ll always get a number between 1 and 6)
• Rolling a 7 is impossible (there is no 7 on a standard dice)
• Rolling an even number is likely (you have 3 even numbers out of 6)
• Rolling a 5 is unlikely (only one way to get it out of six)

Example 3: The Magic Hat

You put a magic hat on your head and pull out a card. The hat contains:

• 5 red cards
• 3 blue cards
• 2 green cards

What’s the chance of pulling out a red card?

There are more red cards than any other colour, so pulling a red card is likely.

Pulling a green card is unlikely because there are fewer green cards.

Try it as a mini adventure

Adventure: The Wizard School Probability Quest

You are a new student at Wizard School. Your teacher gives you a challenge:

Step 1: You have a bag with 3 red marbles, 2 blue marbles, and 1 yellow marble. What is the chance of pulling out a red marble?

Step 2: You roll a dice to see if your spell works. What are the chances of rolling a number between 1 and 6?

Step 3: You are in a magic duel. If you are 80% sure you will win, what does that mean in terms of probability?

Step 4: You are given a magic crystal that can show you the future. What event is certain to happen?

Step 5: What event is impossible in the wizard world?

Step 6: What event is likely to happen when you cast a spell?

Step 7: What event is unlikely to happen when you cast a spell?

Step 8: You have a spell that works 50% of the time. Is this likely or unlikely?

Step 9: If you have 10 spell scrolls and 2 are broken, what is the chance of picking a broken scroll?

Step 10: If you have 100 spell scrolls and 10 are broken, what is the chance of picking a broken scroll?

Common mistakes

• Mistake: Thinking that “unlikely” means it will never happen.

  Why it happens: Children may confuse the words "unlikely" and "impossible".

  Fix: Remind them that "unlikely" means it might happen, but not very often.

• Mistake: Saying that all events are equally likely.

  Why it happens: Children might not notice differences in chance.

  Fix: Ask them to compare groups – for example, “Are there more red or blue marbles?”

• Mistake: Using probability words in the wrong order.

  Why it happens: Confusion with the meaning of words like "certain" and "likely".

  Fix: Practice sorting events from most to least likely.

Parent and carer guide

Help your child understand probability by:

1. Using everyday examples: Ask questions like, “Is it likely to rain today?” or “Is it certain that you’ll eat lunch?”
2. Playing games: Try dice games or card games where you predict outcomes.
3. Looking at real events: Discuss what might happen in a story or a game and how likely it is.
4. Practising sorting: Sort events from impossible to certain to build understanding.
5. Being patient: Probability can be tricky, so don’t rush – let your child explore and make mistakes.

Remember: The goal is not to get perfect answers, but to understand the idea of chance and how we describe it.

Practice questions

1. Is it certain, impossible, likely, or unlikely that you will wake up tomorrow?
2. Is it certain, impossible, likely, or unlikely that a coin will land on heads?
3. Is it certain, impossible, likely, or unlikely that a dice will show a 7?
4. Is it certain, impossible, likely, or unlikely that a baby will grow up to be a wizard?
5. Is it certain, impossible, likely, or unlikely that a cat will be in your room?
6. Is it certain, impossible, likely, or unlikely that a human will fly without wings?
7. Is it certain, impossible, likely, or unlikely that you will get a gold star in class?
8. Is it certain, impossible, likely, or unlikely that a dragon will appear in your garden?
9. Is it certain, impossible, likely, or unlikely that you will have a birthday this year?
10. Is it certain, impossible, likely, or unlikely that you will be 10 years old next year?

Answers:

1. Certain
2. Likely
3. Impossible
4. Likely
5. Unlikely
6. Impossible
7. Likely
8. Impossible
9. Certain
10. Certain

FAQ

What does probability mean?

Probability is a way to describe how likely something is to happen. It can be certain, impossible, likely, or unlikely.

How can I use probability in real life?

You can use probability to make choices, like deciding whether to take an umbrella or what game to play. It helps you think about what might happen next.

Can I use numbers for probability?

Yes! Probability can be shown as numbers like 0 (impossible) to 1 (certain), or as percentages like 50% (half the time).

Why do we need to learn about probability?

Probability helps us make smart choices, understand chance, and predict what might happen. It’s useful in games, science, and everyday life.

What’s the difference between likely and unlikely?

Something that is likely has a good chance of happening, while something that is unlikely has a small chance of happening.