Resources tagged with: Theoretical probability

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

Broad Topics > Probability > Theoretical probability

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?

Stats Statements

Age 16 to 18
Challenge Level

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

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.

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?

The Birthday Bet

Age 14 to 16
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 ?

The Better Choice

Age 14 to 16
Challenge Level

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

Cosy Corner

Age 11 to 14
Challenge Level

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

Two's Company

Age 11 to 14
Challenge Level

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

Odds and Evens

Age 11 to 14
Challenge Level

Are these games fair? How can you tell?

Flippin' Discs

Age 11 to 14
Challenge Level

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

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?

FA Cup

Age 16 to 18
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!

Limiting Probabilities

Age 16 to 18
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.

Put Out

Age 16 to 18
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?

Same or Different?

Age 7 to 11
Challenge Level

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.

Chances Are

Age 14 to 16
Challenge Level

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

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?

Teams

Age 16 to 18
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.

Snooker Frames

Age 16 to 18
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?

Knock-out

Age 16 to 18
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?

Rain or Shine

Age 16 to 18
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.

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?

A Probability Conundrum

Age 14 to 18

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

What Is a Random Variable, Really?

Age 16 to 18

This article offers an advanced perspective on random variables for the interested reader.

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?

Who's the Winner?

Age 14 to 16
Challenge Level

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

Genetics

Age 14 to 16
Challenge Level

A problem about genetics and the transmission of disease.

At Least One...

Age 11 to 14
Challenge Level

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?

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

Find out about 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?

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?

Like Father Like Son

Age 14 to 16
Challenge Level

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

Magic Bag

Age 16 to 18
Challenge Level

A weekly challenge concerning combinatorical probability.

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.

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?

Distribution Differences

Age 14 to 16
Challenge Level

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

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.

Bet You a Million

Age 14 to 16
Challenge Level

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

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?

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?