sample space \(S\) is the set of all possible outcomes of an experiment. It could be continuous or distinct.

## equally likely outcomes

Some sample spaces have equally likely outcomes:

- coin flip
- flipping two coins
- rolling a fair die

If we have equally likely outcomes, \(P(outcome)\) = \(\frac{1}{S}\).

If your sample space has equally likely outcomes, the probability is juts counting:

\begin{equation} P(E) = \frac{count(E)}{count(S)} \end{equation}

Whenever you use this tool, you have to think about whether or not your outcomes are **equally likely**. For instance, the “sum of two dice rolling” is **NOT** equally likely.

Distinct counting makes things equally likely.