Probability

Preliminary Definitions

Below are definitions used extensively throughout the notes.

experiment. An experiment is any procedure that (1) can be repeated, and (2) has a well-defined set of all possible outcomes.

sample space. A sample space is the set of all possible outcomes of an experiment. We denote a sample space with the symbol ${\Omega.}$

event. A subset of the sample space — ergo an outcome set — is called an event. By definition, we say that the result of an experiment is an event. We denote events with in uppercase Latin letters.

simple event. An event comprising just one outcome is called a simple event.

Simple events are also called samples, sample points, or points.

compound event. An event comprising two or more outcomes is called a compound event.

probability. Let ${E}$ be an event where ${E \subset \Omega.}$ The probability of ${E,}$ denoted ${\pb{E},}$ is a ratio of the cardinality of ${E}$ to the cardinality of ${\Omega.}$ That is,