Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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?
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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. . . .
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. . . .
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
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?
This interactivity invites you to make conjectures and explore
probabilities of outcomes related to two independent events.
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 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?
When two closely matched teams play each other, what is the most
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
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.
Engage in a little mathematical detective work to see if you can spot the fakes.
So which is the better bet? Both games cost £1 to play.
Getting two heads and two tails for £3 or £2 for every
six when three dice are rolled.
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. . . .
Two bags contain different numbers of red and blue balls. A ball is
removed from one of the bags. The ball is blue. What is the
probability that it was removed from bag A?
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
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. . . .
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.
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 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;. . . .
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?
Which of these games would you play to give yourself the best possible chance of winning a prize?
A man went to Monte Carlo to try and make his fortune. Whilst he
was there he had an opportunity to bet on the outcome of rolling
dice. He was offered the same odds for each of the. . . .
A problem about genetics and the transmission of disease.
What is the chance I will have a son who looks like me?
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 the probability of winning the Mathsland National
Lottery? Try our simulator to test out your ideas.
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 ?
This set of resources for teachers offers interactive environments
to support probability work at Key Stage 4.
Heads or Tails - the prize doubles until you win it. How much would
you pay to play?
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.
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. . . .