Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Probability - Stage 4

One or Both

Age 14 to 16
ShortChallenge Level Yellow starYellow star

Problem 1 was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Can you work out how many pupils took the exam?

In a Box

Age 14 to 16
Challenge Level Yellow starYellow star

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?

Chances Are

Age 14 to 16
Challenge Level Yellow star

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

The Better Choice

Age 14 to 16
Challenge Level Yellow star

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

Which Spinners?

Age 14 to 18
Challenge Level Yellow star

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

Last One Standing

Age 14 to 16
Challenge Level Yellow star

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

Same Number!

Age 14 to 16
Challenge Level Yellow starYellow star

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

Mathsland National Lottery

Age 14 to 16
Challenge Level Yellow starYellow starYellow star

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

Who's the Winner?

Age 14 to 16
Challenge Level Yellow star

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

Probability Short Problems - Age 14-16

Age 14 to 16

A collection of short problems on probability.

Odds and Evens Made Fair

Age 14 to 16
Challenge Level Yellow starYellow star

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.

Swapping Sweets

Age 14 to 16
ShortChallenge Level Yellow star

If two girls each take a sweet from each other's bags, what is the probability that they end up with what they started with?

Vegtown Elections

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

What percentage of people voted for the Broccoli party in the Vegtown election?

Counting Kangaroos

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

Can you work out how many kangaroos Rachel draws in one colour?

XOXOXO

Age 14 to 16
ShortChallenge Level Yellow starYellow star

6 tiles are placed in a row. What is the probability that no two adjacent tiles have the same letter on them?

Numbers or Letters?

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

Which game offers you the best chance of winning?

Domino Match

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

If you take two dominoes from a set at random, what is the probability that they 'match'?

CD Collection

Age 14 to 16
ShortChallenge Level Yellow starYellow star

How many different ways can I arrange the CDs in my collection?

Flipping Coins

Age 14 to 16
ShortChallenge Level Yellow star

A coin is flipped 4 times. What is the probability of getting heads at least 3 times?

Face Order

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

How many ways can these five faces be ordered?

Winning Marble

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

How can this prisoner escape?

Odd Dice

Age 14 to 16
ShortChallenge Level Yellow starYellow star

These strange dice are rolled. What is the probability that the sum obtained is an odd number?

Dropouts

Age 14 to 16
ShortChallenge Level Yellow starYellow starYellow star

What percentage of students who graduate have never been to France?

Boy or Girl?

Age 14 to 16
ShortChallenge Level Yellow star

Will the witch make a profit or loss?

  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

University of Cambridge logo NRICH logo