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Broad Topics > Probability > Experimental probability

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Odds and Evens Made Fair

Stage: 4 and 5 Challenge Level: Challenge Level:1

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.

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Probably a Code?

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Is the regularity shown in this encoded message noise or structure?

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Time to Evolve 2

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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Which Spinners?

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Random Squares

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is a random pattern?

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The Monte Carlo Method

Stage: 5 Challenge Level: Challenge Level:1

Estimate areas using random grids

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Interactive Spinners

Stage: 3 and 4 Challenge Level: Challenge Level:1

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

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Distribution Maker

Stage: 5 Challenge Level: Challenge Level:1

This tool allows you to create custom-specified random numbers, such as the total on three dice.

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Very Old Man

Stage: 5 Challenge Level: Challenge Level:1

Is the age of this very old man statistically believable?

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It's a Tie

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Epidemic Modelling

Stage: 4 and 5 Challenge Level: Challenge Level:1

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.

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Cosy Corner

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Two's Company

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Domino Pick

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Are these domino games fair? Can you explain why or why not?

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Odds and Evens

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Flippin' Discs

Stage: 3 Challenge Level: Challenge Level:1

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?

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Odds or Sixes?

Stage: 2 Challenge Level: Challenge Level:1

Use the interactivity or play this dice game yourself. How could you make it fair?

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The Twelve Pointed Star Game

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Roll These Dice

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Red or Black Spinner

Stage: Early years, 1, 2, 3 and 4 Challenge Level: Challenge Level:1

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. . . .

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Investigating Epidemics

Stage: 3 and 4 Challenge Level: Challenge Level:1

Simple models which help us to investigate how epidemics grow and die out.

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Who's the Winner?

Stage: 3 Challenge Level: Challenge Level:1

When two closely matched teams play each other, what is the most likely result?

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Lottery Simulator

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

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.

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What Does Random Look Like?

Stage: 3 Challenge Level: Challenge Level:1

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

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The Car That Passes

Stage: 2 Challenge Level: Challenge Level:1

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?

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In the Playground

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?

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Probably ...

Stage: 2 Challenge Level: Challenge Level:1

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.

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Winning the Lottery

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Try out the lottery that is played in a far-away land. What is the chance of winning?

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Mathsland National Lottery

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Same Number!

Stage: 4 Challenge Level: Challenge Level:1

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

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Last One Standing

Stage: 3 and 4 Challenge Level: Challenge Level:1

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

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Sociable Cards

Stage: 3 Challenge Level: Challenge Level:1

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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The Derren Brown Coin Flipping Scam

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Calculate probabilities associated with the Derren Brown coin scam in which he flipped 10 heads in a row.

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X-dice

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Explore these X-dice with numbers other than 1 to 6 on their faces. Which one is best?

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Succession in Randomia

Stage: 5 Challenge Level: Challenge Level:1

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?

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Introducing Distributions

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Misunderstanding Randomness

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Which of these ideas about randomness are actually correct?

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Can't Find a Coin?

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Probability Resources

Stage: 4 Challenge Level: Challenge Level:1

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

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The Random World

Stage: 3, 4 and 5

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.

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Experimenting with Probability

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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;. . . .

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Taking Chances

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Taking Chances Extended

Stage: 4 and 5

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

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Two and One

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

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You Never Get a Six

Stage: 2 Challenge Level: Challenge Level:1

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.

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Tricky Track

Stage: 2 Challenge Level: Challenge Level:1

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?

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The Mean Game

Stage: 5

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.

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Magical Maze - 35 Activities

Stage: 4 and 5

Investigations and activities for you to enjoy on pattern in nature.

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Game of PIG - Ones

Stage: 1 Challenge Level: Challenge Level:1

Play a dice game of chance

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Game of PIG - Sixes

Stage: 2, 3, 4 and 5 Challenge Level: Challenge Level:1

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?