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 generate a set of random results? Can you fool the random simulator?

Can you work out which spinners were used to generate the frequency charts?

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?

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 work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

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?

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

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?

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 five dice are rolled together which do you expect to see more often, no sixes or all sixes ?

This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.

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?

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.

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?

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. . . .

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. . . .

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. . . .

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 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. . . .

This set of resources for teachers offers interactive environments to support probability work at Key Stage 4.

Which of these games would you play to give yourself the best possible chance of winning a prize?

What is the chance I will have a son who looks like me?

Engage in a little mathematical detective work to see if you can spot the fakes.

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?

Heads or Tails - the prize doubles until you win it. How much would you pay to play?

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?

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 ?

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. . . .

How could you compare different situation where something random happens ? What sort of things might be the same ? What might be different ?

A maths-based Football World Cup simulation for teachers and students to use.

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. . . .

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?