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

They look something like this:

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

A set is just a **list of data,** whether it is numbers, colours or something else - so Set A and Set B are just a couple of lists.

**The letter A** is where we put the things that are in set A but not in Set B.

**The letter B** is where we put the things that are in Set B but not in Set A.

**The letter C** is where we put the things that are in **both **lists.

**The letter D** is where we put the things that aren't in either of the two sets.

**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 clubs.

Draw a Venn diagram to illustrate this.

**Set A is the chess club, Set B is the debating club**

We know that there are 2 students in both clubs, so** C = 2**

We know that there are 5 students in the chess club but that 2 of them are also in the debating club.

5 - 2 = 3 This means that **A = 3**

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

So far, we have **A = 3, B = 5 and C = 2.** This accounts for 10 of the 30 students. This means that there are 20 students who are in neither club, so** D = 20**

We can now create our Venn diagram:

We can then use this Venn diagram to calculate the probability of a student selected at random being in a given set.

**Example 2**:

A student is picked at random. What is the chance that he is in the chess club **and **the debating club?

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

Let's have a go at some questions now.