---
title: "sample space"
type: concept
related: [Sample Space, Counting]
source: https://www.jemoka.com/posts/kbhsample_space/
confidence: high
status: active
---

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 &ldquo;sum of two dice rolling&rdquo; is NOT equally likely.
Distinct counting makes things equally likely.
