This package contains environments that offer students the opportunity to move beyond an intuitive understanding of probability. The problems at the start will suit relative beginners to the topic;. . . .

You'll need to work in a group for this problem. The idea is to decide, as a group, whether you agree or disagree with each statement.

Can you generate a set of random results? Can you fool the random simulator?

This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance and is a shorter version of Taking Chances Extended.

Which of these ideas about randomness are actually correct?

Can you work out which spinners were used to generate the frequency charts?

Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

When two closely matched teams play each other, what is the most likely result?

Charlie thinks that a six comes up less often than the other numbers on the dice. Have a look at the results of the test his class did to see if he was right.

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

This is a game for two players. You will need some small-square grid paper, a die and two felt-tip pens or highlighters. Players take turns to roll the die, then move that number of squares in. . . .

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .

All you need for this game is a pack of cards. While you play the game, think about strategies that will increase your chances of winning.

Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.

Think that a coin toss is 50-50 heads or tails? Read on to appreciate the ever-changing and random nature of the world in which we live.

Engage in a little mathematical detective work to see if you can spot the fakes.

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

Try out the lottery that is played in a far-away land. What is the chance of winning?

Use the interactivity or play this dice game yourself. How could you make it fair?

In this game you throw two dice and find their total, then move the appropriate counter to the right. Which counter reaches the purple box first? Is this what you would expect?

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

A maths-based Football World Cup simulation for teachers and students to use.

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

Simple models which help us to investigate how epidemics grow and die out.

What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?