In probability, what does a sample space represent?

• A. The set of all equally likely outcomes
• B. The expected outcome of an event
• C. The average of all outcomes
• D. The outcome that is most likely to occur

Answer: (A)

A sample space in probability is defined as the set of all possible outcomes of a random experiment. This includes every result that can occur when the experiment is performed. By describing the sample space, one can analyze the likelihood of various events occurring. When we refer to "all equally likely outcomes," we are acknowledging that each individual outcome within the sample space has an equal chance of occurring in certain types of problems. This foundational concept is crucial for calculating probabilities and understanding the behavior of random processes.

The other options address different aspects of probability but do not define the sample space itself. For instance, the expected outcome pertains to the average or mean of outcomes weighted by their probabilities, while the most likely outcome refers to the outcome with the highest probability, and the average of all outcomes is a statistical measure that summarizes the center of a distribution but does not encompass the entirety of potential outcomes. Thus, the focus remains clearly on the complete set of possibilities, making the description of the sample space as the set of all equally likely outcomes apt and correct.