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. . . .
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.
Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.
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. . . .
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.
Can you work out which spinners were used to generate the frequency charts?
Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?
When two closely matched teams play each other, what is the most likely result?
If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
Can you generate a set of random results? Can you fool the random simulator?
Which of these ideas about randomness are actually correct?
This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.
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.
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
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.
Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?
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 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. . . .
7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?
Simple models which help us to investigate how epidemics grow and die out.
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
Engage in a little mathematical detective work to see if you can spot the fakes.
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. . . .
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?