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.
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 five dice are rolled together which do you expect to see more
often, no sixes or all sixes ?
Can you work out the probability of winning the Mathsland National
Lottery? Try our simulator to test out your ideas.
This set of resources for teachers offers interactive environments
to support probability work at Key Stage 4.
Imagine a room full of people who keep flipping coins until they
get a tail. Will anyone get six heads in a row?
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.
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. . . .
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
This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.
When two closely matched teams play each other, what is the most
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. . . .
Simple models which help us to investigate how epidemics grow and die out.
Can you generate a set of random results? Can you fool the random
Engage in a little mathematical detective work to see if you can spot the fakes.
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?
If everyone in your class picked a number from 1 to 225, do you
think any two people would pick the same number?
Which of these ideas about randomness are actually correct?
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;. . . .
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Investigations and activities for you to enjoy on pattern in
A maths-based Football World Cup simulation for teachers and students to use.
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.
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?
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. . . .
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. . . .
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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.