This feature offers a new approach to teaching probability.
The articles Probability through Problems outline the thinking behind the approach, and the resources can form the basis of an entire secondary school probability curriculum.
To learn more about the project, see Great Expectations: Probability Through Problems.
list
Probability through problems
Age
11 to 16
Challenge level
This collection of articles for teachers outlines an approach for teaching probability at secondary level.
problem
Which team will win?
Age
11 to 14
Challenge level
A practical experiment which will introduce students to tree diagrams, and help them to understand that outcomes may not be equally likely.
problem
The dog ate my homework!
Age
11 to 16
Challenge level
A practical experiment which uses tree diagrams to help students understand the nature of questions in conditional probability.
problem
Who is cheating?
Age
14 to 16
Challenge level
A practical experiment provides data. Moving onto expected results provides a context to establish the multiplication rule in probability, and an intuitive approach to conditional probability.
problem
Prize giving
Age
14 to 16
Challenge level
What's the fairest way to choose 2 from 8 potential prize winners? How likely are you to be chosen?
problem
The wisdom of the crowd
Age
11 to 16
Challenge level
Who's closest to the correct number of sweets in a jar - an individual guess or the average of many individuals' guesses? Which average?
problem
Capture and recapture
Age
11 to 16
Challenge level
How do scientists or mathematicians estimate the size of a population of wild animals?
problem
How confident are you?
Age
11 to 16
Challenge level
What proportion of people make 90% confident guesses which actually contain the correct answer?
problem
Louis' ice cream business
Age
14 to 16
Challenge level
Should Louis go for the safer options, hoping to limit his losses, or would he be better off with a riskier strategy, focusing on maximising his profit?
problem
To insure or not to insure
Age
14 to 16
Challenge level
Should you insure your mobile phone? It rather depends on whether you focus on the long-term pay-off or the effect of a single event.
This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.
Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.
problem
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?
problem
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.
problem
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?
problem
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?
problem
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.
problem
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?
problem
Statistical shorts
Age
11 to 16
Challenge level
Can you decide whether these short statistical statements are always, sometimes or never true?
problem
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?
problem
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?
problem
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?
Image
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.
This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.
Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.
problem
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?
problem
The better choice
Age
14 to 16
Challenge level
Here are two games you can play. Which offers the better chance of winning?
problem
Which spinners?
Age
14 to 18
Challenge level
Can you work out which spinners were used to generate the frequency charts?
problem
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?
problem
Who's the winner?
Age
14 to 16
Challenge level
When two closely matched teams play each other, what is the most likely result?
problem
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?
problem
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?
problem
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.
problem
Mathsland national lottery
Age
14 to 16
Challenge level
Can you work out the probability of winning the Mathsland National Lottery?
Image
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.