# Sample space

A sample space is the set of all possible outcomes (equally likely) of a probability experiment, typically denoted using set notation. Well-defined sample spaces are a key aspect of of a probabilistic model, along with well-defined events with assigned probabilities. The figure below represents a sample space:

Each event has various possible outcomes with distinct probabilities, all of which are contained within the sample space of the experiment.

A coin toss is an example of a simple experiment. When a coin is tossed, there are two possible outcomes: heads or tails. The sample space for the experiment of tossing a coin is {heads, tails}, or {H, T}.

If there were 3 coins, and order were being considered, there would be 8 events in the ordered sample space: {HHH, HHT, HTH, HTT, TTT, TTH, THT, THH}. If order were not considered, then there would be 6 events in the unordered sample space would be {HHH, HHT, HTT, TTT, TTH, THH}. Each of the subsets of the sample spaces above is an event. For example, "HHH" is an event in either the ordered or unordered sample spaces above.