This article explains how tree diagrams are constructed and helps
you to understand how they can be used to calculate probabilities.
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?
When five dice are rolled together which do you expect to see more
often, no sixes or all sixes ?
Uncertain about the likelihood of unexpected events? You are not
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
If a coin rolls and lands on a set of concentric circles what is
the chance that the coin touches a line ?
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.
A gambler bets half the money in his pocket on the toss of a coin,
winning an equal amount for a head and losing his money if the
result is a tail. After 2n plays he has won exactly n times. Has. . . .
Can you work out which spinners were used to generate the frequency charts?
Can you generate a set of random results? Can you fool the random
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.
Which of these ideas about randomness are actually correct?
This interactivity invites you to make conjectures and explore
probabilities of outcomes related to two independent events.
Under which circumstances would you choose to play to 10 points in
a game of squash which is currently tied at 8-all?
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?
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?
Explore the distribution of molecular masses for various hydrocarbons
You have two bags, four red balls and four white balls. You must
put all the balls in the bags although you are allowed to have one
bag empty. How should you distribute the balls between the two. . . .
The four digits 5, 6, 7 and 8 are put at random in the spaces of
the number : 3 _ 1 _ 4 _ 0 _ 9 2 Calculate the probability that the
answer will be a multiple of 396.
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
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?
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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?
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. . . .
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. . . .
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Here are some examples of 'cons', and see if you can figure out where the trick is.
To win on a scratch card you have to uncover three numbers that add
up to more than fifteen. What is the probability of winning a