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Broad Topics > Probability > Probability

### All Change

##### Age 5 to 7 Challenge Level:

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

### The Hair Colour Game

##### Age 5 to 7 Challenge Level:

The class were playing a maths game using interlocking cubes. Can you help them record what happened?

### Which Spinners?

##### Age 14 to 18 Challenge Level:

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

### 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.

### Scale Invariance

##### Age 16 to 18 Challenge Level:

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

### In a Box

##### Age 14 to 16 Challenge Level:

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 Probability Conundrum

##### Age 14 to 18

What do we mean by probability? This simple problem may challenge your ideas...

### Strange Dice

##### Age 11 to 14 Short Challenge Level:

If two of these unusually numbered dice are thrown, how many different sums are possible?

### Winning Marble

##### Age 14 to 16 Short Challenge Level:

How can this prisoner escape?

### Tools for Thinking about Probability

##### Age 11 to 14 Challenge Level:

Can you design your own probability scale?
How do you describe the different parts?

### What Do You Know about Probability? (2)

##### Age 11 to 14 Challenge Level:

What are the likelihoods of different events when you roll a dice?

### 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. . . .

### Non-transitive Dice

##### Age 11 to 14 Challenge Level:

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

### Twenty20

##### Age 7 to 16 Challenge Level:

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

### Any Win for Tennis?

##### Age 16 to 18 Challenge Level:

What are your chances of winning a game of tennis?

### What's the Point of Squash?

##### Age 14 to 18 Challenge Level:

Under which circumstances would you choose to play to 10 points in a game of squash which is currently tied at 8-all?

### Dicey Decisions

##### Age 16 to 18 Challenge Level:

Can you devise a fair scoring system when dice land edge-up or corner-up?

### Why Do People Find Probability Unintuitive and Difficult?

##### Age 7 to 18

Uncertain about the likelihood of unexpected events? You are not alone!

### Progression in Primary Probability

##### Age 5 to 11

The beginnings of understanding probability begin much earlier than you might think...

### An Introduction to Tree Diagrams

##### Age 11 to 16

This article explains how tree diagrams are constructed and helps you to understand how they can be used to calculate probabilities.

### Probable Words

##### Age 5 to 7 Challenge Level:

If you asked your mum/dad/friend to take you to the park today, what sort of response might you get?

### Do You Feel Lucky?

##### Age 11 to 14 Challenge Level:

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

### Stage 5 Cipher Challenge

##### Age 16 to 18 Challenge Level:

Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?

### Discussing Risk and Reward

##### Age 16 to 18 Challenge Level:

10 starting points for risk vs reward

### Dicey Dice

##### Age 16 to 18 Challenge Level:

Invent a set of three dice where each one is better than one of the others?

### Perfect Eclipse

##### Age 14 to 16 Challenge Level:

Use trigonometry to determine whether solar eclipses on earth can be perfect.

##### Age 16 to 18 Challenge Level:

Use combinatoric probabilities to work out the probability that you are genetically unique!

### Heavy Hydrocarbons

##### Age 14 to 18 Challenge Level:

Explore the distribution of molecular masses for various hydrocarbons

### The Wrong Stats

##### Age 16 to 18 Challenge Level:

Why MUST these statistical statements probably be at least a little bit wrong?

### From A Random World to a Rational Universe

##### Age 7 to 16

In the time before the mathematical idea of randomness was discovered, people thought that everything that happened was part of the will of supernatural beings. So have things changed?

### Coin Lines

##### Age 14 to 16 Challenge Level:

If a coin rolls and lands on a set of concentric circles what is the chance that the coin touches a line ?

### How Random!

##### Age 7 to 11 Challenge Level:

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

### Misunderstanding Randomness

##### Age 11 to 14 Challenge Level:

Which of these ideas about randomness are actually correct?

### 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?

### Three Spinners

##### Age 7 to 11 Challenge Level:

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

### 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.

### Count the Beat

##### Age 5 to 11

This article, written by Nicky Goulder and Samantha Lodge, reveals how maths and marimbas can go hand-in-hand! Why not try out some of the musical maths activities in your own classroom?

### 396

##### Age 14 to 16 Challenge Level:

The four digits 5, 6, 7 and 8 are put at random in the spaces of the number : 3 _ 1 _ 4 _ 0 _ 9 2 Calculate the probability that the answer will be a multiple of 396.

### Con Tricks

##### Age 11 to 14

Here are some examples of 'cons', and see if you can figure out where the trick is.

### Scissors, Paper, Rock

##### Age 5 to 7 Challenge Level:

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

### 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.

### Racing Odds

##### Age 11 to 14 Challenge Level:

In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?

### Nine or Ten?

##### Age 11 to 14 Short Challenge Level:

Is a score of 9 more likely than a score of 10 when you roll three dice?

##### Age 11 to 14 Challenge Level:

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.

### The Lady or the Lions

##### Age 11 to 14 Challenge Level:

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. . . .

### Scratch Cards

##### Age 14 to 16 Challenge Level:

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?

### Fixing the Odds

##### Age 14 to 16 Challenge Level:

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. . . .

### Win or Lose?

##### Age 14 to 16 Challenge Level:

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. . . .