How is a sample space used to list the possible results of a probability experiment?

In probability and statistics, a sample space (often denoted by S) is the set of all possible outcomes of a random experiment. It serves as the foundational framework for the experiment, representing every potential result as an individual point within the set.123

How the Sample Space Functions

• Defining Outcomes: The sample space lists every distinct, possible result that can occur during a trial. For example, tossing a single coin results in a sample space of {heads, tails}, while tossing two dice results in a sample space of 36 ordered pairs, such as (1, 1) or (6, 6).3
• Identifying Events: An event is defined as a specific subset of the sample space. By identifying which outcomes within the sample space satisfy the conditions of an event, you can calculate its probability.3
• Calculating Probability: For experiments with equally likely outcomes, the probability of an event is the ratio of the number of favorable outcomes (those within the event subset) to the total number of outcomes in the sample space.3
• Handling Complexity: The sample space allows for the use of the principle of additivity, where the probability of a complex event is calculated by summing the probabilities of the individual outcomes that compose it.24