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.
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.
This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.
Imagine a room full of people who keep flipping coins until they
get a tail. Will anyone get six heads in a row?
This set of resources for teachers offers interactive environments
to support probability work at Key Stage 4.
When five dice are rolled together which do you expect to see more
often, no sixes or all sixes ?
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.
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
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. . . .
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. . . .
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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.
If everyone in your class picked a number from 1 to 225, do you
think any two people would pick the same number?
Engage in a little mathematical detective work to see if you can spot the fakes.
Can you generate a set of random results? Can you fool the random
Simple models which help us to investigate how epidemics grow and die out.
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.
When two closely matched teams play each other, what is the most
Which of these ideas about randomness are actually correct?
This interactivity invites you to make conjectures and explore
probabilities of outcomes related to two independent events.
Can you work out which spinners were used to generate the frequency charts?
This package contains environments that offer students the
opportunity to move beyond an intuitive understanding of
probability. The problems at the start will suit relative beginners
to the topic;. . . .
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?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
Investigations and activities for you to enjoy on pattern in
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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. . . .
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.
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. . . .
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?