Real World Maths Adventures
The fairground probability question prompts
Adult prompts and extension questions for use spinners and dice to explore fair and unfair games without gambling.
Quick answer
You can use spinners and dice to explore fair and unfair games by looking at whether all outcomes are equally likely, and whether the game gives everyone the same chance to win.Learning outcome
By the end of this page, you will understand how to tell if a game is fair or unfair using probability, and you can create your own fair or unfair games using spinners or dice. Success signs:- You can say whether a game is fair or unfair by looking at the chances of winning
- You can make a spinner or dice game that is fair
- You can explain why one game is more likely to win than another
- You can use words like "likely", "unlikely", "equal chance", and "impossible" to describe your games
Why this matters
Probability helps us understand how likely something is to happen. When we play games, we often want to know if the game is fair or not. If a game is fair, everyone has the same chance to win. If it's unfair, one player has a better chance. Understanding this helps you make better choices, whether you're playing with friends or planning a party game. You can use probability in real life too. For example, if you're picking a prize from a box, you can think about how likely you are to get a big prize or a small one. Probability is also used in science, weather forecasts, and even in making video games fair for everyone.How it works
Probability is about how likely something is to happen. We can use spinners or dice to explore this. 1. Make a spinner or use a dice – You can make a spinner with different sections or use a regular 6-sided dice. 2. Decide what counts as a win – For example, landing on red or rolling a 6. 3. Count how many ways you can win – How many sections or numbers are winners? 4. Count how many total options there are – How many sections or numbers are there altogether? 5. Compare the two numbers – If there are more ways to win than not to win, the game is more likely to be fair or even a little bit unfair in your favour. If there are more ways not to win, it's unfair.Examples you can see
Let’s imagine you are at a fairground with a spinner game. The spinner has 6 sections: 3 red, 2 blue, and 1 green. Example 1: Is this game fair? - If you win by landing on red, how many ways can you win? 3 - How many sections are there in total? 6 - So the chance of winning is 3 out of 6. - That’s the same as 1 out of 2, or 50%. - If the game was fair, everyone should have the same chance. - So, if it’s red that wins, it's a fair game because there’s an equal chance of landing on red or not red. Example 2: What if you win by landing on green? - How many ways can you win? 1 - How many sections are there? 6 - So the chance of winning is 1 out of 6. - That’s a very small chance, so it's an unfair game because it’s very unlikely you’ll win. Example 3: Using a dice - You roll a dice and win if you get a number greater than 4. - Numbers greater than 4: 5 and 6 = 2 ways to win - Total numbers on dice: 6 - So, 2 out of 6 = 1 out of 3 chance to win - This is a fair game because it’s not too hard or too easy to win.Try it as a mini adventure
Adventure: The Fairground Game Challenge You are the game designer at a fun fair. You have to make two games using spinners or dice. Game 1: The Lucky Spinner - Make a spinner with 4 sections. - 2 sections are red, 1 is blue, and 1 is yellow. - If you land on red, you win a prize. - Is this a fair game? Game 2: The Dice Race - Roll a dice. - If you roll a 3 or 4, you win. - Is this a fair game? Step-by-step challenge: 1st time: Make your spinner or dice. 2nd time: Decide what counts as a win. 3rd time: Count how many ways you can win. 4th time: Count how many total options there are. 5th time: Compare the two numbers. 6th time: Decide if the game is fair or unfair. 7th time: Explain why. Mini challenge: If you roll a dice, what is the chance of rolling an even number? What about an odd number?Common mistakes
- Mistake: Thinking that a game is fair just because it uses a dice or spinner. Why it happens: Children often think that just because a game uses a spinner or dice, it must be fair. Fix: Always check if the number of winning options is the same as the number of losing options.
- Mistake: Counting the same option twice. Why it happens: When counting, children can accidentally count a red section twice. Fix: Label each section or number clearly, and count once only.
- Mistake: Not comparing the number of wins to the total number of options. Why it happens: Some children only count the wins without thinking about how many total options there are. Fix: Always ask, “How many ways can I win?” and “How many total options are there?”
- Mistake: Believing that a game is unfair just because it’s hard to win. Why it happens: Children may think that if you can’t win easily, the game is unfair. Fix: A game is unfair if one player has a much better chance than others, not just because it’s hard.
Parent and carer guide
Parents and carers can help by asking questions and encouraging children to think about their games. What to say: - “How many ways can you win?” - “What is the chance of landing on blue?” - “Is it fair that you have a 1 in 6 chance to win?” - “What would happen if we changed the game?” How to help: - Let your child make their own spinner or dice game. - Encourage them to test the game a few times and see if it feels fair. - Use everyday objects like coins or bottle caps to explore probability. - If your child says something is unfair, ask them to explain why. What not to worry about: - It's normal for children to get confused at first. - It’s okay if they don’t get it right the first time. - Probability can be tricky, but it gets easier with practice.Practice questions
- How many ways can you win if you spin a spinner with 8 sections and win on 3 of them?
- Is a game fair if you roll a dice and win by rolling a 1 or 2?
- If you have a spinner with 5 sections and 2 are winners, is the game fair?
- How many total outcomes are there when rolling a dice?
- If you win by rolling an even number on a dice, how many ways can you win?
- 3 ways
- Yes, it is fair because 2 out of 6 is the same as 1 out of 3
- No, it’s unfair because 2 out of 5 is not the same as 1 out of 2
- 6 outcomes
- 3 ways (2, 4, 6)
FAQ
What does it mean for a game to be fair?
A fair game is one where everyone has the same chance to win.
How do I know if a spinner is fair?
If all the sections are the same size, the spinner is fair. If one section is bigger, it’s more likely to land on that section, so it’s unfair.
Can I make a fair game with an unfair spinner?
Yes! You can make rules so that even if the spinner is unfair, the game is still fair. For example, you can say that landing on a big section counts as 2 wins.
What does "probability" mean?
Probability is how likely something is to happen. It can be described as a fraction, like 1 in 6, or words like "likely" or "unlikely".
How can I use this in real life?
You can use probability when choosing a prize from a box, picking a card from a deck, or even deciding who goes first in a game.