  # Use Frequency Trees

In this worksheet, students practise drawing and using frequency trees to solve probability problems. Key stage:  KS 4

GCSE Subjects:   Maths

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

Curriculum topic:   Probability

Curriculum subtopic:   Probability Basic Probability and Experiments

Difficulty level:   #### Worksheet Overview

There are a number of ways to record multiple event probabilities, you can use probability trees, sample space diagrams or two-way tables.

Today, we'll look at another type of diagram that can be used to record the outcomes for two or more events... frequency trees.

Frequency trees are just used to classify information. Let's look at a couple to illustrate this point.

Example 1:

60 people are members of a gym. Of these 45 are male.

Draw a frequency tree to show this information.

We can see here that there is only 1 piece of information (the gender) so we only need a one branch frequency tree. Each 'branch' of the tree will have one of the options. We can now start building our tree. We know that there are 60 people in total, so we place this information in the first space. We also know that we have 45 males. Which means we must have 15 females. Example 2: In a class of 32 students, 18 are boys of which 7 are left-handed.

There are 15 left-handed people in the class altogether.

If I pick a student at random, what is the probability it is a right-handed girl?

We can see there are 2 options here, Gender and left-handed/right-handed. This means we need a two-level frequency tree, Once we have the structure. We can start working out what goes where.

We have 32 students, if 18 are male, this means 14 must be female.

We are told that 7 of the boys are left-handed so, 11 of the boys must be right-handed.

We are also told that there are 15 left-handed people altogether if 7 boys are left-handed then 8 girls must be.

This leaves us with 6 right-handed girls. We can now finally answer our probability question.

We know we have 6 right-handed girls out of the 32 students which gives a probability of...

 6 32
=
 3 16

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