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Broad Topics > Probability > Theoretical probability

### Stats Statements

##### Stage: 5 Challenge Level:

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

### Introducing Distributions

##### Stage: 4 Challenge Level:

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

### 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.

### The Derren Brown Coin Flipping Scam

##### Stage: 5 Challenge Level:

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

### Like Father Like Son

##### Stage: 4 Short Challenge Level:

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

### Coin Tossing Games

##### Stage: 4 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. . . .

### Genetics

##### Stage: 4 Challenge Level:

A problem about genetics and the transmission of disease.

### FA Cup

##### Stage: 5 Challenge Level:

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!

### Distribution Differences

##### Stage: 4 Challenge Level:

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

### Scratch Cards

##### Stage: 4 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?

### 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.

### Probability Resources

##### Stage: 4 Challenge Level:

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

### Win or Lose?

##### Stage: 4 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. . . .

### Snooker

##### Stage: 5 Challenge Level:

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

### Squash

##### Stage: 5 Challenge Level:

If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?

### Fixing the Odds

##### Stage: 4 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. . . .

### Succession in Randomia

##### Stage: 5 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?

### Teams

##### Stage: 5 Challenge Level:

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

### Gambling at Monte Carlo

##### Stage: 4 Challenge Level:

A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?

### Which Spinners?

##### Stage: 4 Challenge Level:

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

### Last One Standing

##### Stage: 4 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?

### Who's the Winner?

##### Stage: 4 Challenge Level:

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

### Rain or Shine

##### Stage: 5 Challenge Level:

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.

### Mathsland National Lottery

##### Stage: 4 Challenge Level:

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

### Weekly Challenge 37: Magic Bag

##### Stage: 5 Challenge Level:

A weekly challenge concerning combinatorical probability.

### Same Number!

##### Stage: 4 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?

### Marbles and Bags

##### Stage: 4 Challenge Level:

Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?

### The Birthday Bet

##### Stage: 4 Challenge Level:

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 ?

### Put Out

##### Stage: 5 Challenge Level:

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?

### Knock-out

##### Stage: 5 Challenge Level:

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?

##### Stage: 4 and 5 Challenge Level:

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?

### Playing Squash

##### Stage: 5

Playing squash involves lots of mathematics. This article explores the mathematics of a squash match and how a knowledge of probability could influence the choices you make.

### Chances Are

##### Stage: 4 Challenge Level:

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

### Bet You a Million

##### Stage: 4 Challenge Level:

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

### Limiting Probabilities

##### Stage: 5 Challenge Level:

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.

##### Stage: 4 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. . . .

### The Better Bet

##### Stage: 4 Challenge Level:

Here are two games you have to pay to play. Which is the better bet?

### Football World Cup Simulation

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

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

### Card Game (a Simple Version of Clock Patience)

##### Stage: 4 Challenge Level:

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .

### In a Box

##### Stage: 4 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?

### How Many Balls?

##### Stage: 5 Challenge Level:

A bag contains red and blue balls. You are told the probabilities of drawing certain combinations of balls. Find how many red and how many blue balls there are in the bag.

### Snooker Frames

##### Stage: 5 Challenge Level:

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?