In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.
What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
Is the regularity shown in this encoded message noise or structure?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Can you work out which spinners were used to generate the frequency charts?
What is a random pattern?
Estimate areas using random grids
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
This tool allows you to create custom-specified random numbers, such as the total on three dice.
Is the age of this very old man statistically believable?
Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
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?
7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?
Are these domino games fair? Can you explain why or why not?
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
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?
Use the interactivity or play this dice game yourself. How could you make it fair?
Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .
Simple models which help us to investigate how epidemics grow and die out.
When two closely matched teams play each other, what is the most likely result?
Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.
Engage in a little mathematical detective work to see if you can spot the fakes.
You'll need to work in a group for this problem. The idea is to decide, as a group, whether you agree or disagree with each statement.
Try out the lottery that is played in a far-away land. What is the chance of winning?
Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.
If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Calculate probabilities associated with the Derren Brown coin scam in which he flipped 10 heads in a row.
Explore these X-dice with numbers other than 1 to 6 on their faces. Which one is best?
By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?
When five dice are rolled together which do you expect to see more often, no sixes or all sixes ?
Which of these ideas about randomness are actually correct?
Can you generate a set of random results? Can you fool the random simulator?
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.
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.
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
Charlie thinks that a six comes up less often than the other numbers on the dice. Have a look at the results of the test his class did to see if he was right.
In this game you throw two dice and find their total, then move the appropriate counter to the right. Which counter reaches the purple box first? Is this what you would expect?
Edward Wallace based his A Level Statistics Project on The Mean Game. Each picks 2 numbers. The winner is the player who picks a number closest to the mean of all the numbers picked.
Play a dice game of chance
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
This is a game for two players. You will need some small-square grid paper, a die and two felt-tip pens or highlighters. Players take turns to roll the die, then move that number of squares in. . . .
All you need for this game is a pack of cards. While you play the game, think about strategies that will increase your chances of winning.