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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

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.

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