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There are **67** NRICH Mathematical resources connected to **Theoretical probability**, you may find related items under Probability.

Problem
Primary curriculum
Secondary curriculum
### Who's the Winner?

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### At Least One...

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What Does Random Look Like?

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Car That Passes

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### In the Playground

What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mathsland National Lottery

Can you work out the probability of winning the Mathsland National Lottery?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Same Number!

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Last One Standing

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Stats Statements

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Which Spinners?

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

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Interactive Spinners

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### It's a Tie

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Birthday Bet

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 ?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Better Choice

Here are two games you can play. Which offers the better chance of winning?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cosy Corner

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two's Company

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Flippin' Discs

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Twelve Pointed Star Game

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### FA Cup

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!

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Limiting Probabilities

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Put Out

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Same or Different?

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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Chances Are

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### In a Box

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Teams

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Snooker Frames

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Knock-out

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rain or Shine

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Roll These Dice

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bet You a Million

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two and One

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tricky Track

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Voting Paradox

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?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Many Balls?

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.

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Playing Squash

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.

Age 16 to 18

Game
Primary curriculum
Secondary curriculum
### Football World Cup Simulation

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

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Bit of a Dicey Problem

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Trick or Treat

Mrs. Smith had emptied packets of chocolate-covered mice, plastic frogs and gummi-worms into a cauldron for treats. What treat is Trixie most likely to pick out?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bipin's Choice

Bipin is in a game show and he has picked a red ball out of 10 balls. He wins a large sum of money, but can you use the information to decided what he should do next?

Age 7 to 11

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Problem
Primary curriculum
Secondary curriculum
### Thank Your Lucky Stars

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 corner of the grid?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Nine or Ten?

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

Age 11 to 14

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Scratch Cards

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fixing the Odds

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 bags so as to make the probability of choosing a red ball as small as possible and what will the probability be in that case?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Win or Lose?

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 he more money than he started with?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Coin Tossing Games

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 a head (you win). What is the probability that you win?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Marbles and Bags

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Gambling at Monte Carlo

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Snooker

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Squash

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?

Age 16 to 18

Challenge Level