  # Use Venn Diagrams for Probability

In this worksheet, students use Venn diagrams to sort data and find simple probabilities. 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

A Venn diagram is something you will have probably seen before. It's two circles that crossover in the middle.

They look something like this. How and why?

This does look a bit complicated to start with until you dig down what it all means.

A set is just a list of data, be it numbers, colours or something else. So Set A and Set B are just a couple of lists.

B is the things that are in both lists.

A is what is in set A but not Set B

C is what is in Set B but not in Set A

D are the things that aren't in either.

Example: In a class of 30 students, 5 are in the chess club and 7 are in the debating club. There are 2 students who are in both.

Draw a Venn diagram to illustrate this. - Set A is the chess club, Set B is the debating club

- We know there are 2 students in both, so B = 2

- We know there are 5 in the chess club and that 2 are also in the debating club. This means A = 3

- We know there are 7 in the debating club but that 2 of them are also in the chess club. This means that C = 5

- So far, we have A = 3, B = 2 and C = 5. This accounts for 10 of the 30 students. This means D = 20

We can now create our Venn diagram. Example 2: A student is picked at random, what is the chance he is in the chess club and the debating club.

There are only two students that work here, this gives our probability as 2/30 which equals 1/15

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