Sample Space and Events

The sample space is the complete list of every possible outcome of a random situation, and an event is any subset of those outcomes you care about. For one die roll the sample space is {1,2,3,4,5,6}, and “rolling an even number” is the event {2,4,6}.

Naming the sample space first is the discipline that keeps probability honest: you compute the probability of an event by adding up the chances of the outcomes inside it. Forgetting an outcome, or double-counting one, is the most common beginner mistake.