In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

When two closely matched teams play each other, what is the most likely result?

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by. . . .

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

Can you generate a set of random results? Can you fool the random simulator?

Which of these ideas about randomness are actually correct?

Can you work out which spinners were used to generate the frequency charts?

This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance and is a shorter version of Taking Chances Extended.

This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.

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.

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

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. . . .

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

Engage in a little mathematical detective work to see if you can spot the fakes.

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

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.

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. . . .

A maths-based Football World Cup simulation for teachers and students to use.

This is a game for two players. You will need some small-square grid paper, a die and two felt-tip pens or highlighters. Players take turns to roll the die, then move that number of squares in. . . .

Simple models which help us to investigate how epidemics grow and die out.

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?