Basic Definitions

Experiments/Outcomes

An experiment generates an outcome from a pre-determined list. For example, a dice roll generates outcomes in the set \(\{1, 2, 3, 4, 5, 6\}\)

Sample Space

The sample space, denoted \(\Omega\), is the set of possible outcomes. Note that the probability of this event is 1, since something in the sample space will always occur.

Event

An event is a subset of the sample space, or a collection of possible outcomes of an experiment. We say that the event has occurred if any of the outcomes in the event have happened.

Naive Definition of Probability

If all outcomes are equally likely, the probability of an event \(A\) happening is:

\[ P_{\textrm{naive}}(A) = \frac{\textnormal{number of outcomes favorable to $A$}}{\textnormal{number of outcomes}} \]