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 set of resources for teachers offers interactive environments
to support probability work at Key Stage 4.
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. . . .
A problem about genetics and the transmission of disease.
What is the chance I will have a son who looks like me?
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.
Here are two games you have to pay to play. Which is the better bet?
When five dice are rolled together which do you expect to see more
often, no sixes or all sixes ?
Heads or Tails - the prize doubles until you win it. How much would
you pay to play?
If everyone in your class picked a number from 1 to 225, do you
think any two people would pick the same number?
When two closely matched teams play each other, what is the most likely result?
Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?
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 work out which spinners were used to generate the frequency charts?
How could you compare different situation where something random
happens ? What sort of things might be the same ? What might be
The next ten people coming into a store will be asked their
birthday. If the prize is £20, would you bet £1 that two
of these ten people will have the same birthday ?
Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10. What about the case of 3 dice? Is a score of 9 more likely then a score of 10 with 3 dice?
Which of these games would you play to give yourself the best possible chance of winning a prize?
Four fair dice are marked differently on their six faces. Choose first ANY one of them. I can always choose another that will give me a better chance of winning. Investigate.
The King showed the Princess a map of the maze and the Princess was
allowed to decide which room she would wait in. She was not allowed
to send a copy to her lover who would have to guess which path. . . .
A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?
Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?
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. . . .
Which of these ideas about randomness are actually correct?
Can you generate a set of random results? Can you fool the random
A maths-based Football World Cup simulation for teachers and students to use.
Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over...
You win if all your cards end up in the trays before you run out of cards in. . . .
What are the likelihoods of different events when you roll a dice?
Some relationships are transitive, such as `if A>B and B>C
then it follows that A>C', but some are not. In a voting system,
if A beats B and B beats C should we expect A to beat C?
Can you design your own probability scale?
How do you describe the different parts?
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. . . .
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
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?
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?
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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?
Engage in a little mathematical detective work to see if you can spot the fakes.