A probability space is defined by two things: \(\Omega\) and \(p.\)

- \(\Omega\) is the set of all possible outcomes. Can be finite or infinite
- Each element \(\omega\in\Omega\) is a single outcome
- Each experiment produces a unique outcome
- The distribution \(p:\Omega\to\mathbb R\) is a function such that \[0\leq p(\omega)\leq 1\quad \forall \omega\in\Omega\\ \sum_{\omega\in\Omega}p(\omega)=1\]