Age 12 guide to probability
Age-appropriate activities, explanations and practice ideas for probability.
Quick answer
Probability is how likely something is to happen, and it's shown as a number between 0 and 1, or as a percentage. You can work out probability by counting the number of ways something can happen compared to all possible outcomes.
Learning outcome
By the end of this page, you will be able to:
- Understand what probability means in everyday life
- Calculate simple probability using fractions
- Use words like "certain", "impossible", "likely", and "unlikely" to describe chance
- Compare different probabilities and see which events are more or less likely
Why this matters
Probability helps us understand chance and make good guesses about what might happen next. You use probability every day without even realising it! When you guess if it will rain tomorrow, or if you'll get a red sweet from a bag, or if you'll win a game – you're using probability. It's useful in games, science, weather forecasts, and even in choosing what to eat for lunch.
How it works
Probability is about how likely something is to happen. We show this with numbers from 0 to 1, or sometimes as percentages. Here's how to think about it:
- Think of all the possible things that could happen (these are called outcomes).
- Count how many of those outcomes are what you want (these are called favourable outcomes).
- Divide the number of favourable outcomes by the total number of outcomes.
The result is the probability of your event happening. For example, if you roll a dice, there are 6 possible outcomes (1, 2, 3, 4, 5, 6). If you want to roll a 3, there is 1 favourable outcome (rolling a 3) out of 6 possible outcomes. So the probability is 1/6.
Examples you can see
Let's look at some examples to make this clearer:
Example 1: Rolling a dice
When you roll a normal dice, there are 6 faces: 1, 2, 3, 4, 5, 6.
What is the probability of rolling a 4?
- Number of ways to roll a 4 = 1
- Total number of outcomes = 6
- Probability = 1/6
Example 2: Drawing a card
In a standard deck of 52 cards, there are 13 hearts.
What is the probability of drawing a heart?
- Number of hearts = 13
- Total number of cards = 52
- Probability = 13/52 = 1/4
Example 3: Flipping a coin
When you flip a coin, there are 2 sides: heads and tails.
What is the probability of getting tails?
- Number of tails = 1
- Total number of outcomes = 2
- Probability = 1/2
Real-world example: Choosing a snack
Imagine you have a jar with 5 apples, 3 bananas, and 2 oranges. You pick one fruit at random.
- Total fruits = 5 + 3 + 2 = 10
- Probability of picking an apple = 5/10 = 1/2
- Probability of picking a banana = 3/10
- Probability of picking an orange = 2/10 = 1/5
So, you're most likely to pick an apple because there are more apples than any other fruit.
Try it as a mini adventure
Adventure: The Probability Treasure Hunt
You are a treasure hunter and need to find a hidden treasure. But there are clues at each step, and you must choose the most likely path to follow. Each clue leads to a new decision with two or more options. You need to calculate the probability of each path to find the treasure!
Step 1: You find a map with two paths: Path A and Path B. Path A has 4 stones and Path B has 6 stones. You must choose a path with the fewest stones to go faster.
- Path A: 4 stones
- Path B: 6 stones
- Best path = Path A (fewer stones)
Step 2: You see a chest with 3 locks. You have 1 key for each lock. What is the probability of opening the chest if you guess the right lock?
- Number of locks = 3
- Number of correct locks = 1
- Probability = 1/3
Step 3: You hear a sound. You can either go left or right. If you go left, you have a 2/5 chance of finding a clue. If you go right, you have a 3/5 chance of finding a clue. Which way should you go?
- Left: 2/5 chance
- Right: 3/5 chance
- Better choice = Right (higher probability)
Common mistakes
- Mistake: Thinking that all outcomes are equally likely.
- Why it happens: Children sometimes assume that because there are 3 outcomes, each has a 1/3 chance. But if one outcome is more likely, like rolling a 6 on a loaded dice, that's not true.
- Fix: Always check if outcomes are really equal or if some are more likely than others.
- Mistake: Forgetting to count all possible outcomes.
- Why it happens: When working with probability, it's easy to miss some outcomes. For example, in a bag with 3 red and 2 blue balls, a child might only count red balls.
- Fix: List all possible outcomes clearly before calculating.
- Mistake: Using percentages when the answer should be a fraction.
- Why it happens: Some children are more comfortable with percentages and forget that probability can be shown as a fraction.
- Fix: Remember that 1/2 is the same as 50%, but always show the fraction first when asked.
Parent and carer guide
As a parent or carer, you can help your child understand probability by:
- Using everyday situations to talk about chance, like "It might rain today" or "I might win the game".
- Playing games that involve probability, like rolling dice or spinning wheels.
- Encouraging your child to think about how many ways something can happen before calculating the chance.
- Practising with simple examples, like flipping coins or picking sweets from a bag.
- Checking that they understand the difference between chance and certainty.
Don't worry if your child makes mistakes – probability is tricky at first. The more they practice, the more confident they'll become.
Practice questions
- Question: What is the probability of rolling a 5 on a six-sided dice?
- Answer: 1/6
- Question: A bag has 4 red marbles and 6 blue marbles. What is the probability of picking a red marble?
- Answer: 4/10 = 2/5
- Question: What is the probability of flipping a coin and getting heads?
- Answer: 1/2
- Question: There are 3 green apples and 7 red apples. What is the probability of picking a red apple?
- Answer: 7/10
- Question: What is the probability of drawing a king from a deck of 52 cards?
- Answer: 4/52 = 1/13
FAQ
What is probability?
Probability is a way to measure how likely something is to happen. It's shown as a number between 0 and 1, or as a percentage.
How do I calculate probability?
To calculate probability, divide the number of ways something can happen by the total number of possible outcomes.
What does "certain" and "impossible" mean in probability?
"Certain" means something will definitely happen, so its probability is 1. "Impossible" means it will never happen, so its probability is 0.
Why is probability useful?
Probability helps us make smart choices, understand the world, and predict what might happen in games, science, and daily life.
Can probability be more than 1?
No, probability is always between 0 and 1. If it's more than 1, something is wrong with the calculation.