Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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. . . .
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?
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 work out which spinners were used to generate the frequency charts?
Which of these ideas about randomness are actually correct?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Can you generate a set of random results? Can you fool the random
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?
Use the interactivity or play this dice game yourself. How could
you make it fair?
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
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;. . . .
A maths-based Football World Cup simulation for teachers and students to use.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Imagine a room full of people who keep flipping coins until they
get a tail. Will anyone get six heads in a row?
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?
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. . . .
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.
Engage in a little mathematical detective work to see if you can spot the fakes.
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.
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.
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
When two closely matched teams play each other, what is the most
Can you work out the probability of winning the Mathsland National
Lottery? Try our simulator to test out your ideas.
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?
Simple models which help us to investigate how epidemics grow and die out.
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.
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
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?