130. Sample Space

A probability model begins with two tasks:

1. Specify the set of all possible outcomes

2. Specify beliefs about how likely each outcome is

The Sample Space

• The sample space, denoted by $\mathrm{\Omega }$, is the set of all possible outcomes of an experiment

• The elements of $\mathrm{\Omega }$, called outcomes, must satisfy:

  • Mutually exclusivity: No two distinct outcomes can occur simultaneously

  • Collective exhaustiveness: Every possible result of the experiment must be included in $\mathrm{\Omega }$