Do you go to any clubs at your school?

Year 9 students were asked what after-school club they go to: chess or debating.

The results are illustrated in the following **Venn diagram**:

What is the probability that a student picked at random goes to both?

We can see that there are 2 students in the 'overlap', i.e. the **intersection**.

If we call the sets of students who go to chess and debating C and D, respectively, then we can denote it using $∩:$

**$C ∩ D$**$= 2$

There are 3 + 2 + 5 + 20 = 30 students altogether.

So the probability that a student picked at random goes to both clubs is:

**P($C ∩ D) = 2/30 = 1/15$**

Similarly, how could we find the probability that a student picked at random goes to chess or debating?

First things first!

In maths, when we say 'or', we don't mean 'either ... or ...' we mean '**... or ... or both'.**

This means that when we want students who go to chess **or** debating, we want those who go only to chess, only to debating *or to both*.

We call the set of these students the **union** (it is the two circles 'united' together!).

We denote this using the symbol $∪ (easy to remember - it looks a 'u' as in 'union'!)$.

So here we have:

**C **$∪ D =$3 + 2 + 5 = 10

So 10 out of 30 students go to chess or debating.

That means the probability that a student picked at random goes to chess or debating is:

**P(C $∪ D$) = 10/30 = 1/3**

Let's have a go at some questions!