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Broad Topics > Probability > Experimental probability

### 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.

### 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?

### 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?

### Probably a Code?

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

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

### 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?

### 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.

### Very Old Man

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

Is the age of this very old man statistically believable?

### 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?

### 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?

### 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?

### Domino Pick

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

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

### 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?

### 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?

### Odds or Sixes?

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

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

### 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?

### 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 possible answers?

### 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. . . .

### Investigating Epidemics

##### Age 11 to 16 Challenge Level:

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

### Who's the Winner?

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

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

### 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.

### 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.

### 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.

### 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?

### 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.

### 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?

### 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?

### 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?

### 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.

### 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?

### 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?

### 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?

### 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.

### 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.

### 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.

### 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?

### 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.

### 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?

### 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.

### 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. . . .

### 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.

### Football World Cup Simulation

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

A maths-based Football World Cup simulation for teachers and students to use.

### Thank Your Lucky Stars

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

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

### 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. . . .

### Coin Tossing Games

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

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by. . . .