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Use Sample Space Diagrams

In this worksheet, students will practise listing all the outcomes of events by using a sample space diagram.

'Use Sample Space 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

What is a sample space diagram?

They are used to show all the outcomes of two events where the events are equally likely.

For example, you could use a sample space diagram when you roll dice, flip coins etc.

 

What does it look like?

All sample space diagrams have the same form - the outcomes for each event go along the top and the side, and the outcomes for the combined events go in the middle.

 

A sample space diagram

 

How do we fill one of these in?

This is easiest if we use an example:

I roll a dice and add the numbers together.

Draw a sample space diagram to show all the outcomes.

 

Step 1: Set up the outcomes for the individual events.

We know that on each dice we have the numbers 1 to 6.

 

A sample space diagram

 

Step 2: Fill in the middle.

I'll start with a random one - we are told that we add the numbers. If we roll two fours and add,

we will get 8.

 

A sample space diagram

 

We can now fill in the rest.

 

A sample space diagram

 

Will they always have numbers in the middle?

It depends on the question. For example, the outcomes of rolling a dice and flipping a coin can't be added together, so we just write both the outcomes.

 

A sample space diagram

 

 

Using a sample space diagram to find probabilities.

 

Example:

I roll two dice and add them together.

What is the chance that my numbers add to make a prime number?

 

We already know that the sample space diagram looks like the one above. If we want to find the probability that my result is a prime, we count all the ones that are prime.

 

A sample space diagram

 

From this, we can count that we have 15 prime numbers.

We have 36 numbers in the middle section (we don't count the outside numbers).

This gives a probability of 15/36 which can cancel to 5/12

 

Now let's have a go at some questions.

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