Probability Trees

'Use what you already to know to see just how and why probability tree diagrams work'

Probability is a topic that moves very quickly from that which is easily understood and intuitive to something seemingly much more complex. Sample space diagrams, probability trees, fractions decimals, 'and' rules, 'or' rules and so on..... It is easy to lose track of what it all means and to understand how all of these things are inter related. In this activity the aim is for you to demonstrate to yourselves the link between all of the things that you know. In doing so you should see how a sample space diagram and a tree diagram effectively do the same thing and understand why sometimes you multiply and sometimes you add probabilities. The activity demands some revision of fraction manipulation and hopefully demonstrates why a tree diagram, once understood, is the more versatile tool for lots of problems. The activity might take between 2 - 3 hours to complete and involves puzzles, challenges, and practice!


This activity aims to bridge the gap between sample space and tree diagrams for combined events.


There are quite a few resources required for this activity and they are all saved as Google docs linked to below. (Documents are set to print in A4 - The 'For computers' links at the end link to Google docs that can be saved locally for editing). Below there are some previews of some of the worksheets. There are also some  Probability Trees teacher notes

 Part 1 - Sample Space - Practise working out the possible outcomes for combined events. For computers

 Part 2 - Fractions and Multiplying - Here are some tasks with a set of fractions that relevant to the problem. This will need printing, copying and cutting out. (unless you work on computers) For computers

 Part 3 - Fractions and adding - More related problems with the fractions. For Computers

 Part 4 - The tree Diagram - Link it all together, use the sample space diagram to help you build a tree diagram and see the links between the previous activities. For computers

 Part 5 - Practice! - Put what you have learned in to practice with these fill in the gap probability tree diagrams. (you are given a little bit less information each time. For computers

Activity in action

Here are some photos of the activity in action.

Probability Trees - Part 1

Probability Trees - Part 2

Multiplying Fractions - The 'and' rule.

Probability Trees - Part 5

This worksheet represents the 'End Goal' of the activity.


Here follows an outline of what the task is. If students are not reading this page then the teacher will need to show and give this overview.

The activity is outlined clearly on the different sheets linked to above.

  • Part 1 - Sample Space
  • Part 2 - Fractions and Multiplying
  • Part 3 - Fractions and adding
  • Part 4 - Tree diagrams
  • Part 5 - Probability trees (practice)

I did it my way!

As a practising maths teacher I know that most of us like to give activities our own little twist and do them 'our way'. It would be great to add a little collect of 'twists' from users. You can either add your twist to the comments section below or e-mail them directly to me at In time, some of these twists may appear here....

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