Sample spaces are really important when we look at probabilities in theory.

What is a sample space?

It's just a list of all the possible results from an experiment.

For example, think about flipping a coin. The sample space would be:

{Heads, Tails}.

When you want to find probabilities, you use sample spaces to see which outcomes are equally likely.

Take rolling a six-sided die, for instance.

The sample space for that would be:

{1, 2, 3, 4, 5, 6}.

Each of these numbers has the same chance of showing up.

To find the probability of something happening, you can use this simple formula:

P(A) = Number of outcomes you want / Total number of outcomes.

Let's say you want to find the chance of rolling an odd number.

The odd numbers on a die are 1, 3, and 5. That's three outcomes you want out of the six possible outcomes.

So you calculate it like this:

P(Odd) = 3 / 6 = 1 / 2.

This means there's a 50% chance of rolling an odd number.

If you don't clearly define your sample space, you could end up with the wrong probability!