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Broad Topics > Probability > Theoretical probability

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Stats Statements

Stage: 5 Challenge Level: Challenge Level:1

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

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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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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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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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The Birthday Bet

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

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 ?

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The Better Bet

Stage: 4 Challenge Level: Challenge Level:1

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.

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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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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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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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FA Cup

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

In four years 2001 to 2004 Arsenal have been drawn against Chelsea in the FA cup and have beaten Chelsea every time. What was the probability of this? Lots of fractions in the calculations!

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Limiting Probabilities

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

Given probabilities of taking paths in a graph from each node, use matrix multiplication to find the probability of going from one vertex to another in 2 stages, or 3, or 4 or even 100.

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Put Out

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

After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?

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Same or Different?

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

Anna and Becky put one purple cube and two yellow cubes into a bag to play a game. Is the game fair? Explain your answer.

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Chances Are

Stage: 4 Challenge Level: Challenge Level:1

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

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In a Box

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

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?

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Teams

Stage: 5 Challenge Level: Challenge Level:1

Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.

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Snooker Frames

Stage: 5 Challenge Level: Challenge Level:1

It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?

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Knock-out

Stage: 5 Challenge Level: Challenge Level:1

Before a knockout tournament with 2^n players I pick two players. What is the probability that they have to play against each other at some point in the tournament?

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Rain or Shine

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

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

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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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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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Genetics

Stage: 4 Challenge Level: Challenge Level:1

A problem about genetics and the transmission of disease.

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At Least One...

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

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?

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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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Like Father Like Son

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

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

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Weekly Challenge 37: Magic Bag

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

A weekly challenge concerning combinatorical probability.

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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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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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Distribution Differences

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

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

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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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Bet You a Million

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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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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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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Voting Paradox

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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?