In the time before the mathematical idea of randomness was discovered, people thought that everything that happened was part of the will of supernatural beings. So have things changed?
Some people offer advice on how to win at games of chance, or how
to influence probability in your favour. Can you decide whether
advice is good or not?
This article explains how tree diagrams are constructed and helps
you to understand how they can be used to calculate probabilities.
Uncertain about the likelihood of unexpected events? You are not
Can you work out which spinners were used to generate the frequency charts?
This article, written by Nicky Goulder and Samantha Lodge, reveals
how maths and marimbas can go hand-in-hand! Why not try out some of
the musical maths activities in your own classroom?
Which of these ideas about randomness are actually correct?
Can you generate a set of random results? Can you fool the random
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.
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
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
This interactivity invites you to make conjectures and explore
probabilities of outcomes related to two independent events.
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?
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.
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. . . .
Bluey-green, white and transparent squares with a few odd bits of
shapes around the perimeter. But, how many squares are there of
each type in the complete circle? Study the picture and make. . . .
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. . . .
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?
The beginnings of understanding probability begin much earlier than
you might think...
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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?
Here are some examples of 'cons', and see if you can figure out where the trick is.
Explore this interactivity and see if you can work out what it
does. Could you use it to estimate the area of a shape?