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probability

Dice probability

Explore outcomes from one die and simple dice games.

Quick answer

When you roll one dice, there are 6 possible outcomes – the numbers 1, 2, 3, 4, 5, and 6. Each number has an equal chance of appearing.

Learning outcome

By the end of this page, you will understand that when you roll one dice, each number has the same chance of coming up, and you can use this to predict simple outcomes in games. Success signs:
  • You can say which numbers are on a dice
  • You can explain that each number has an equal chance of appearing
  • You can play a simple dice game and predict what might happen
  • You can tell a friend how to use dice to make fair games

Why this matters

Probability is about how likely something is to happen. When you play board games, card games, or even just roll dice for fun, you’re using probability. Understanding dice probability helps you make better choices in games and helps you understand how things work in the world. Whether you're deciding if it's safe to go outside, guessing what your friend will roll, or planning your next move in a game, knowing about probability helps you think more clearly.

How it works

A dice is a cube with six faces. Each face shows a different number from 1 to 6. When you roll a dice, it lands on one of these faces. The chance of landing on any one number is the same. This is called a fair dice. Here’s how to think about it:
  1. There are 6 possible outcomes: 1, 2, 3, 4, 5, 6
  2. Each outcome has an equal chance
  3. If you roll the dice many times, each number should come up about the same number of times

Examples you can see

Let’s imagine you roll a dice once.
  • You could roll a 1
  • You could roll a 2
  • You could roll a 3
  • You could roll a 4
  • You could roll a 5
  • You could roll a 6
All of these outcomes are equally likely. So, the chance of rolling any one number is 1 in 6, or about 16.67%. Now let’s look at a simple example with two dice. If you roll two dice, you can get different combinations. For example, rolling a 3 and a 4 is one way. Rolling a 2 and a 5 is another way. But there are many more combinations. Each die still has 6 possible outcomes, so two dice together have 6 x 6 = 36 possible outcomes. Here is a table showing how many ways you can roll each number with two dice:
Sum Ways to roll it Number of ways
2 (1,1) 1
3 (1,2), (2,1) 2
4 (1,3), (2,2), (3,1) 3
5 (1,4), (2,3), (3,2), (4,1) 4
6 (1,5), (2,4), (3,3), (4,2), (5,1) 5
7 (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) 6
8 (2,6), (3,5), (4,4), (5,3), (6,2) 5
9 (3,6), (4,5), (5,4), (6,3) 4
10 (4,6), (5,5), (6,4) 3
11 (5,6), (6,5) 2
12 (6,6) 1
You can see that rolling a 7 is the most likely sum because there are 6 ways to make it.

Try it as a mini adventure

Let’s go on a dice adventure! You are a detective trying to solve a mystery. A treasure chest is locked and you need to roll a dice to open it. The chest only opens if you roll a number that is higher than 3.
  1. First, you roll the dice and get a 2. Did you open the chest?
  2. Next, you roll again and get a 5. Did you open the chest this time?
  3. Then, you roll again and get a 1. Did you open the chest?
  4. Finally, you roll again and get a 6. Did you open the chest?
Let’s count the numbers that are higher than 3:
  • 4, 5, 6 are higher than 3
  • So, you have a 3 in 6 chance of opening the chest each time
You can also try this with a friend. Roll the dice and see how many times you get a number higher than 3 in 10 rolls. Record your results and see if it matches the chance.

Common mistakes

  • Mistake: Thinking that rolling a 6 is more likely than rolling a 1.
    Why it happens: Children sometimes think that some numbers are "luckier" or more special.
    Fix: Remind them that each number on a fair dice has the same chance of appearing.
  • Mistake: Believing that if you roll a dice 6 times, you will get each number once.
    Why it happens: This is a misunderstanding of chance – it’s not about fairness over time, but about probability.
    Fix: Explain that over many rolls, each number should come up roughly the same number of times, but not necessarily in a specific pattern.
  • Mistake: Thinking that rolling a dice is completely random and that you can't predict anything.
    Why it happens: Children might not yet understand that probability helps us predict what is likely to happen.
    Fix: Use examples like "rolling a 6 is less likely than rolling a 4 or 5" to show that we can make predictions.

Parent and carer guide

Parents and carers can help by:
  • Playing dice games together to make probability fun
  • Using everyday situations to talk about chance, like “What are the chances of rain today?”
  • Encouraging children to make predictions and check them with dice
  • Using dice to teach concepts like fairness and equal chance
  • Not worrying if a child gets confused – probability is a big idea that takes time to understand
To help your child at home:
  1. Roll a dice and ask, “What number do you think you’ll get?”
  2. Try rolling it 10 times and write down the results
  3. Ask, “Do you think it’s more likely to roll an even number or an odd number?”
  4. Use a dice to play simple games like “Roll a 4 or higher to win”

Practice questions

  1. What is the chance of rolling a 3 on one dice?
  2. If you roll a dice 12 times, how many times would you expect to roll a 1?
  3. What is the chance of rolling a number greater than 4?
  4. Can you list all the possible outcomes when rolling one dice?
  5. How many possible outcomes are there when rolling two dice?
Answers:
  1. 1 in 6 or about 16.67%
  2. 12 ÷ 6 = 2 times
  3. 2 in 6 or about 33.33% (numbers 5 and 6)
  4. 1, 2, 3, 4, 5, 6
  5. 36 possible outcomes (6 x 6)

FAQ

What is probability?

Probability is how likely something is to happen. For example, when you roll a dice, there is a chance of rolling any number from 1 to 6.

Why is it important to learn about dice probability?

Learning about dice probability helps you understand games, make predictions, and make better decisions. It’s also useful in science, engineering, and even in daily life.

How many outcomes are there when rolling one dice?

There are 6 possible outcomes: 1, 2, 3, 4, 5, and 6.

What is the chance of rolling an even number on one dice?

There are 3 even numbers (2, 4, 6) out of 6 possible outcomes, so the chance is 3 in 6 or 50%.

Can you use dice to make fair games?

Yes! If you use a fair dice, each number has the same chance of appearing, which makes games fair. For example, you can decide that rolling a 6 wins a prize, and rolling any other number means you try again.