Module 10 Probability

Graphs - Sequences - Teacher Notes

Solvemymaths has produced pages like this for lots of topics


NRICH: Various Venns
NRICH: Carroll Diagrams 
More Carroll Diagrams 
What Shape and Colour?
NRICH: In a Box 

NRICH: Domino Pick
Odds or Sixes?
Twelve Pointed Star Game
Same or Different?
NRICH: Cipher Frequency Analysis 
Substitution Cipher
Toying with Spinners
The Better Bet
NRICH: Birthday Bet

Shodor: Racing Game
Monty Hall Problem



Probability is one of those topics that appeals to all learners because it can be approached practically.

For example:

Which team will win?  -  Click here

Every weekend, Team Beaver and Team Yeti play each other at 2-Goal Football - they play until two goals have been scored.  Sometimes games last only a minute or two, sometimes they seem to go on for ever.

Over a 36-week season, which team is likely to win more games? 

This activity is really well structured with excellent supporting worksheet – Click here and Click here

NRICH: KS2/3 Accessible Activities

NRICH: KS3/4 Accessible Activities

NRICH: KS4/5 Accessible Activities


Online Interactive Resources

Single 6, 8, 10 or 12 Sides Virtual Dice where you can number as you wish – Single Spin option only – Click here

One – Two or Three Six Sided Dice – Click here

Multiple Dice and Adjustable Spinners – Click here


Listing Outcomes

Non Transitive Dice

These are a set of 3 or more dice where A beats B, B beats C but C beats A!
For the 5 Dice -
Click here
For the solution –
Click here

Great for some relative frequency work before drawing up the sample space to explore the theoretical probabilities - Click here for more details

Sicherman Dice

These are the only dice which have the same expected outcomes as a pair of ordinary dice.  Get pupils to explore possibilities or give them the 12 numbers and see whether they can place them on the correct dice – Click here for more details


Listing Outcomes - Combining Probabilities

Design a Game

 This simple problem was posed by Daniel Finkel:

Consider this simple game: flip a fair coin twice. You win if you get two heads, and lose otherwise. It’s not hard to calculate that the chances of winning are 1/4… . Your challenge is to design a game, using only a fair coin, that you have a 1/3 chance of winning.

Finkel continues, "And here is my recipe for getting the most out of this problem: if you can solve it, do not stop with one answer. Rather, see how many answers you can come up with. I’ve posed this problem to many people, and I continue to hear novel solutions."

Here are three familiar solutions (I notice these also turned up quickly in readers' comments to the NYT!):

§  Toss the coin until the first head appears. You win if this takes an even number of tosses

§  Toss the coin twice. You win on HH and lose on HT or TH. If TT appears, ignore the result and make another two tosses.

§  Toss the coin until the first appearance of HTT or HHT on consecutive tosses. You win HTT.


[Thanks to Jo @mathsjam]

Simple probability match-up -

Frog race - Flash Maths

Experimental vs Theoretical probability activity

Probability and words - Median Don Steward

Evaluating Statements about Probability - Maths Assessment Project (activities at the back)

Introduction to probability - lessons plans and activities - Project Maths

Introduction to relative frequency - lessons plans and activities - Project Maths

Simple probability trees worksheet (& solutions) - adapted from original by Georgian Burgess

Probability trees for dependent events