In probability, the sample space is all the possible results from a random experiment.

Here are some important parts to know:

• Outcomes: These are the individual results of an experiment. For example, when you roll a die, the possible outcomes are 1, 2, 3, 4, 5, or 6.

• Events: These are groups of outcomes. For example, if we want to look for rolling an even number, our event would include 2, 4, and 6.

Let’s look at a simple example.

When you roll a die, the sample space, which shows all possible outcomes, is:
S = {1, 2, 3, 4, 5, 6}.

Now, how do we figure out the chance of getting a specific outcome?

We use this formula:
P(event) = (Number of favorable outcomes) ÷ (Total outcomes).

So if we want to know the chance of rolling a 4, we look at the number of times we can get that 4. That’s just 1 time, since there's only one 4 on the die.

The total number of outcomes when rolling a die is 6 (since there are 6 faces on it).

So, the chance of rolling a 4 would be:
P(4) = 1 (for the 4) ÷ 6 (total outcomes) = 1/6.

Now you know how sample space works!