sample space

A sample space is the set of all possible outcomes of a statistical experiment. For instance, when tossing a coin once, the sample space consists of two outcomes: "heads" and "tails". If you toss two dice, there are 36 possible outcomes, each represented as an ordered pair (e.g., (1, 2) is distinct from (2, 1)).12

Probability theory uses these sample spaces to understand the likelihood of specific events. An event is a subset of the sample space. For example, the event "the sum of the faces showing on two dice equals six" includes outcomes like (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1). Probability theory provides the framework for calculating the chances of these events occurring, which has applications in fields like opinion polls and clinical trials.2