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?
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?
Which of these games would you play to give yourself the best possible chance of winning a prize?
What do we mean by probability? This simple problem may challenge your ideas...
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 article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.
A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?
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 ?
Here are two games you can play. Which offers the better chance of winning?
If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
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 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. . . .
Are these games fair? How can you tell?
What are the likelihoods of different events when you roll a dice?
Can you generate a set of random results? Can you fool the random simulator?
Which of these ideas about randomness are actually correct?
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 different ?
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.
What is the chance I will have a son who looks like me?
Can you design your own probability scale?
How do you describe the different parts?
Can you work out the probability of winning the Mathsland National Lottery?
Heads or Tails - the prize doubles until you win it. How much would you pay to play?
Is a score of 9 more likely than a score of 10 when you roll three dice?
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
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. . . .
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. . . .
Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?
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.
When two closely matched teams play each other, what is the most likely result?
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?
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 prize?
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.
A problem about genetics and the transmission of disease.
Six balls are shaken. You win if at least one red ball ends in a corner. 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. . . .