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Broad Topics > Probability > Experimental probability

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Odds and Evens Made Fair

Age 14 to 16 Challenge Level:

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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The Car That Passes

Age 7 to 11 Challenge Level:

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

Age 5 to 11 Challenge Level:

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 a Code?

Age 16 to 18 Challenge Level:

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

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Time to Evolve 2

Age 16 to 18 Challenge Level:

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?

Age 14 to 18 Challenge Level:

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

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Random Squares

Age 16 to 18 Challenge Level:

What is a random pattern?

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The Monte Carlo Method

Age 16 to 18 Challenge Level:

Estimate areas using random grids

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Interactive Spinners

Age 11 to 14 Challenge Level:

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

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Distribution Maker

Age 16 to 18 Challenge Level:

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

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Very Old Man

Age 16 to 18 Challenge Level:

Is the age of this very old man statistically believable?

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It's a Tie

Age 7 to 11 Challenge Level:

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

Age 14 to 18 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 5 to 7 Challenge Level:

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

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Odds and Evens

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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?

Age 7 to 11 Challenge Level:

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

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The Twelve Pointed Star Game

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

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

Age 3 to 16 Challenge Level:

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

Age 11 to 16 Challenge Level:

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

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Who's the Winner?

Age 14 to 16 Challenge Level:

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

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Lottery Simulator

Age 7 to 16 Challenge Level:

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?

Age 11 to 14 Challenge Level:

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

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Probably ...

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

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

Age 14 to 16 Challenge Level:

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!

Age 14 to 16 Challenge Level:

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

Age 14 to 16 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 16 to 18 Challenge Level:

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

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X-dice

Age 16 to 18 Challenge Level:

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

Age 16 to 18 Challenge Level:

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

Age 14 to 16 Challenge Level:

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

Age 11 to 14 Challenge Level:

Which of these ideas about randomness are actually correct?

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Can't Find a Coin?

Age 11 to 14 Challenge Level:

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

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Probability Resources

Age 14 to 16 Challenge Level:

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

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The Random World

Age 11 to 18

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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Taking Chances

Age 11 to 14 Challenge Level:

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

Age 14 to 18

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

Age 5 to 7 Challenge Level:

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

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

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

Age 16 to 18

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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Game of PIG - Ones

Age 5 to 7 Challenge Level:

Play a dice game of chance

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Game of PIG - Sixes

Age 7 to 18 Challenge Level:

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

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Snail Trails

Age 11 to 14 Challenge Level:

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. . . .

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Stop or Dare

Age 7 to 16 Challenge Level:

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.