10 starting points for risk vs reward
Uncertain about the likelihood of unexpected events? You are not alone!
If a coin rolls and lands on a set of concentric circles what is the chance that the coin touches a line ?
This tool allows you to create custom-specified random numbers, such as the total on three dice.
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.
Under which circumstances would you choose to play to 10 points in a game of squash which is currently tied at 8-all?
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. . . .
How can this prisoner escape?
Can you devise a fair scoring system when dice land edge-up or corner-up?
What are your chances of winning a game of tennis?
Explore the distribution of molecular masses for various hydrocarbons
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.
Is a score of 9 more likely than a score of 10 when you roll three dice?
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.
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?
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. . . .
What do we mean by probability? This simple problem may challenge your ideas...
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. . . .
When five dice are rolled together which do you expect to see more often, no sixes or all sixes ?
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.
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 bit wrong?
Use combinatoric probabilities to work out the probability that you are genetically unique!
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
Can you work out which spinners were used to generate the frequency charts?
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.
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?
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?