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. . . .
Invent a set of three dice where each one is better than one of the others?
This article explains how tree diagrams are constructed and helps
you to understand how they can be used to calculate probabilities.
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
Can you work out which spinners were used to generate the frequency charts?
When five dice are rolled together which do you expect to see more
often, no sixes or all sixes ?
This interactivity invites you to make conjectures and explore
probabilities of outcomes related to two independent events.
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.
Can you devise a fair scoring system when dice land edge-up or corner-up?
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. . . .
Uncertain about the likelihood of unexpected events? You are not
If a coin rolls and lands on a set of concentric circles what is
the chance that the coin touches a line ?
Under which circumstances would you choose to play to 10 points in
a game of squash which is currently tied at 8-all?
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
Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?
10 starting points for risk vs reward
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 tool allows you to create custom-specified random numbers,
such as the total on three dice.
What are your chances of winning a game of tennis?
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
Use combinatoric probabilities to work out the probability that you
are genetically unique!
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.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
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?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Why MUST these statistical statements probably be at least a little