Sample Spaces

First some definitions:

Probability: subdiscipline in math that focuses on the study of randomness/uncertainty
Experiment: Any action/activity whose outcome is subject to uncertainty

Then we say the following:

The Sample Space of an Experiment

The sample space of an experiment, denoted by $S$ , is the set of all possible outcomes of that experiment

3 Coin Flips

Consider an example where we filp a coin, where $H$ is heads, and $T$ is ails. The sample space $S = {H, T}$
If we had a coin be flipped 3 consecutive times, then the sample space becomes:

S = {H H H, H H T, H T H, H T T, T H H, T H T, T T H, T T T}

Example

$S$ can represent a continuous range too. If a customer is buying gasoline in the range of 0 to 50 USD, then $S = [0, 50]$ . But we have to be specific, since a dollar amount is needed here (to the nearest hundreth). Really we only have:

S = {0, . . ., 49.99, 50.00}

We have have $S$ be a set of tuples to represent two outcomes happening simultaneously. For example $(2, 5)$ might represent the event of finding 2 dollars on the street while also finding 5 birds on the street (the events don't have to relate necessarily).

References

[[Matthew A. Carlton, Jay L. Devore - Probability with STEM Applications-Wiley (2020).pdf#page=36]]