Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Apply Algebra to Tree Diagrams

In this worksheet, students will apply algebra to tree diagrams.

'Apply Algebra to Tree Diagrams' worksheet

Key stage:  KS 4

Year:  GCSE

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Probability

Curriculum subtopic:   Probability Combined Events and Probability Diagrams

Difficulty level:  

Worksheet Overview

So far, we have looked at using tree diagrams to find the outcome of multiple events when we are given the probability of a single event.

Now we need to look at doing this the other way round.


Example 1:

A bag contains red and blue balls. A ball is picked out, the colour noted and then replaced. This is repeated.

If the probability of picking out two red balls is 1/25, what is the probability of picking out two blue balls?


Step 1: Let's put this into a tree diagram:

A tree diagram


Step 2: What can we work out?

We know that the probabilities are the same for each event because we are told  that the ball is replaced.

If we know that P(RR) = 1/25, this is the same as saying P(R) x P(R) = 1/25 so P(R) = 1/5


A tree diagram


Step 3: Work out the other event.

We know that A and B are exhaustive, so P(B) must equal 4/5


A tree diagram


Step 4: Complete the rest of the tree diagram.


A tree diagram

Step 5: Use this to answer the question.

We were initially asked for the probability of two blue balls. From the tree diagram, we can now see that this is 16/25


Let's move on to some questions now.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started

Try an activity or get started for free

  • National Tutoring Awards 2023 Shortlisted / Parents
    National Tutoring Awards 2023 Shortlisted
  • Private-Tutoring-WINNER-EducationInvestor-Awards / Parents
    Winner - Private Tutoring
  • Bett Awards Finalist / Parents
  • Winner - Best for Home Learning / Parents
    Winner - Best for Home Learning / Parents