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