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. . . .
What do we mean by probability? This simple problem may challenge your ideas...
Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.
Heads or Tails - the prize doubles until you win it. How much would you pay to play?
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 ?
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.
Which of these games would you play to give yourself the best possible chance of winning a prize?
How could you compare different situation where something random happens ? What sort of things might be the same ? What might be different ?
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?
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 man went to Monte Carlo to try and make his fortune. Is his strategy a winning 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.
When two closely matched teams play each other, what is the most likely result?
Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?
Here are two games you have to pay to play. Which is the better bet?
Is a score of 9 more likely than a score of 10 when you roll three dice?
This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.
What are the likelihoods of different events when you roll a dice?
Can you design your own probability scale?
How do you describe the different parts?
Which of these ideas about randomness are actually correct?
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.
Can you generate a set of random results? Can you fool the random simulator?
What is the chance I will have a son who looks like me?
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?
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. . . .
If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
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?
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
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?
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
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?
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. . . .
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. . . .
A maths-based Football World Cup simulation for teachers and students to use.
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?
A problem about genetics and the transmission of disease.
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 the corner?
Engage in a little mathematical detective work to see if you can spot the fakes.