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Maths Adventures

Detective maths quest: probability

A story-led junior maths adventure using evidence, charts and mystery patterns to talk about likely, unlikely, certain and impossible events.

Quick answer

Probability is about how likely something is to happen – from certain events that always happen, to impossible events that never happen, and everything in between like likely or unlikely.

Learning outcome

By the end of this page, you will be able to sort events as certain, likely, unlikely, or impossible, and explain why. Success signs:
  • You can name one event that is certain, one that is impossible, one that is likely, and one that is unlikely.
  • You can explain why you think an event is more or less likely to happen.
  • You can use words like "certain", "impossible", "likely", and "unlikely" in your sentences.
  • You can make a simple chart showing how events fit into these categories.

Why this matters

Probability helps you think about what might happen in the future. It's useful when you're playing games, guessing what's in a mystery box, or deciding if you should take an umbrella. Detectives use probability to figure out which suspect is most likely to have done something, or which clue is most important. Probability helps you make better decisions and solve mysteries!

How it works

Probability is about chance – how sure we are that something will happen. We can think of it like this:
  • Certain: Something that will definitely happen (100% chance)
  • Impossible: Something that will never happen (0% chance)
  • Likely: Something that has a good chance of happening
  • Unlikely: Something that has a small chance of happening
Let’s look at how we can sort events into these groups.

Examples you can see

Here are some real-life examples to help you understand probability: 1. Certain Events
  • It will be daytime if it is morning.
  • Every person has a heartbeat.
  • When you drop a ball, it will fall down.
2. Impossible Events
  • A human can fly without a plane.
  • A cat can lay eggs.
  • You can find a purple elephant in the zoo.
3. Likely Events
  • It will rain in the UK in the next month.
  • You will eat breakfast tomorrow.
  • You will see a car on the road.
4. Unlikely Events
  • You will win the lottery.
  • You will meet a famous celebrity today.
  • You will find a gold coin in your pocket.
Imagine you are a detective. You find a note that says: “The thief will be here at 3 o’clock.” Is this likely, unlikely, certain, or impossible? It depends on how much information you have. If you know the thief always comes at 3 o’clock, it’s certain. If you know the thief never comes at 3 o’clock, it’s impossible. If you don’t know, it might be likely or unlikely.

Try it as a mini adventure

Adventure: The Mystery of the Missing Cake You are a detective in a school kitchen. The cake is missing, and you need to solve the mystery. Here’s what you know:
  • The cake was in the fridge at 10am.
  • Someone took it out at 11am.
  • It was a big cake, so it was hard to hide.
  • No one saw who took it.
Now, you must sort these events:
  1. Someone took the cake out of the fridge at 11am.
  2. The cake will be found in the fridge tomorrow.
  3. The cake was in the fridge at 10am.
  4. Someone will eat the cake today.
Sort each one into one of the four categories: certain, impossible, likely, or unlikely. Answers:
  1. Someone took the cake out of the fridge at 11am – Likely
  2. The cake will be found in the fridge tomorrow – Unlikely
  3. The cake was in the fridge at 10am – Certain
  4. Someone will eat the cake today – Likely

Common mistakes

  • Mistake: Thinking that “likely” means “will definitely happen.”
    Why it happens: Children often confuse likelihood with certainty.
    Fix: Remember, likely means it has a good chance, but it might not happen.
  • Mistake: Saying that impossible means “very unlikely.”
    Why it happens: Some children think impossible is just a very small chance.
    Fix: Impossible means it will never happen, not just that it’s rare.
  • Mistake: Mixing up the words "certain" and "likely."
    Why it happens: The words sound similar, and both describe events that probably happen.
    Fix: Certain means it will happen, likely means it has a good chance but not 100%.

Parent and carer guide

As a parent or carer, you can help by:
  • Asking your child to give examples of events they think are certain, impossible, likely, or unlikely.
  • Playing games where you guess what will happen next, like rolling dice or flipping coins.
  • Using real-life situations like weather or school events to talk about probability.
  • Encouraging your child to explain their thinking when sorting events.
  • Not worrying if they mix up words at first – it's part of learning!
Try this with your child: “Is it likely that it will snow in summer? Why or why not?” Listen to their answer and ask them to explain their thinking.

Practice questions

  1. Is it certain, impossible, likely, or unlikely that you will eat lunch today?
  2. Is it certain, impossible, likely, or unlikely that a dog will lay eggs?
  3. Is it certain, impossible, likely, or unlikely that you will see a rainbow after rain?
  4. Is it certain, impossible, likely, or unlikely that you will win a million pounds in the lottery?
  5. Is it certain, impossible, likely, or unlikely that the sun will rise tomorrow?
Answers:
  1. Likely
  2. Impossible
  3. Likely
  4. Unlikely
  5. Certain

FAQ

What does probability mean?

Probability is how likely something is to happen. We use words like certain, impossible, likely, and unlikely to describe it.

Can events be both likely and unlikely?

No, each event belongs in one category. If something is likely, it's not also unlikely, and vice versa.

How do I know if something is impossible?

Something is impossible if it can never happen, no matter what. For example, humans can’t fly without a plane.

Is it harder to guess probability for big events?

Yes, it can be harder to guess the probability of big events like winning the lottery, but we can still sort them into categories.

Can I use probability in games?

Absolutely! Probability helps us understand what might happen in games, like rolling a die or drawing a card.