When we throw a coin and roll a die, how many possible outcomes are there?

We can organise the outcomes using a table:

We can see that there are 12 possible outcomes for these **combined events** (i.e. multiple events occurring at the same time).

The set of all outcomes is called the **sample space**.

But is there a faster way to find out the number of items in the **sample space**?

Yes, there is!

A coin has 2 possible outcomes and a die has 6.

We can get how many possible outcomes there are for both the coin and the die by multiplying the number of possible outcomes for each:

2 x 6 = 12

Which is what we got by listing them before!

Let's say we are now throwing two dice and recording their **sum.**

Each die has 6 possible outcomes.

So the number of all possible outcomes is:

6 x 6 = 36

Can we see how that is so much faster than listing them all?!

Sometimes it is useful to generate the whole sample space though.

In that case, a table is generally what we would use so as not to forget any outcomes!

Ready to have a go at some questions?!