Sample Space

The Sample Space $\Omega$ is the collection of all possible outcomes from an experiment. If we are rolling a six sided die, then $\Omega = \left\{ 1,2,3,4,5,6\right\}$ , If we are flipping a coin $\Omega = \left\{ \text{Heads,Tails}\right\}$ , etc.

A outcome or sample point of $\Omega$ is a single element of $\Omega$ , we will usually refer to outcomes as $\omega$ or possibly $x$ .

An event is a subset of $\Omega$ . So an event is a collection of outcomes. When we discuss probability we will be discussing the probability of particular events occuring.

Note: It is possible, and perfectly fine, for an event to contain a single outcome.

Once we have the idea of Sample Space, outcomes, and events we can begin to place more structure on these objects, so next we move onto Sigma Algebras.

Sample Space
Sigma Algebras
Basic Theorems