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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
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?
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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?
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?
A maths-based Football World Cup simulation for teachers and students to use.
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
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?
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?
Engage in a little mathematical detective work to see if you can spot the fakes.
Can you generate a set of random results? Can you fool the random
Which of these ideas about randomness are actually correct?
When two closely matched teams play each other, what is the most
Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10. What about the case of 3 dice? Is a score of 9 more likely then a score of 10 with 3 dice?
The King showed the Princess a map of the maze and the Princess was
allowed to decide which room she would wait in. She was not allowed
to send a copy to her lover who would have to guess which path. . . .
Four fair dice are marked differently on their six faces. Choose first ANY one of them. I can always choose another that will give me a better chance of winning. Investigate.
Can you work out which spinners were used to generate the frequency charts?
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
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.
Bipin is in a game show and he has picked a red ball out of 10
balls. He wins a large sum of money, but can you use the
information to decided what he should do next?
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
This interactivity invites you to make conjectures and explore
probabilities of outcomes related to two independent events.
Anna and Becky put one purple cube and two yellow cubes into a bag
to play a game. Is the game fair? Explain your answer.
Mrs. Smith had emptied packets of chocolate-covered mice, plastic
frogs and gummi-worms into a cauldron for treats. What treat is
Trixie most likely to pick out?
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;. . . .
Chris and Jo put two red and four blue ribbons in a box. They each
pick a ribbon from the box without looking. Jo wins if the two
ribbons are the same colour. Is the game fair?
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.
Imagine a room full of people who keep flipping coins until they
get a tail. Will anyone get six heads in a row?
Imagine flipping a coin a number of times. Can you work out the
probability you will get a head on at least one of the flips?