In probability theory, what is meant by "sample space"?

• A. The set of all possible outcomes of a random experiment
• B. The total number of trials performed
• C. The average of all possible outcomes
• D. The most likely outcome from a set of events

Answer: (A)

The concept of "sample space" in probability theory refers to the complete set of all possible outcomes that can result from a random experiment. This is foundational in probability, as it provides the framework within which probabilities are assigned to different events. An event is a specific subset of the sample space, and understanding the sample space enables you to analyze the likelihood of various outcomes occurring.

For example, if you were to consider the experiment of rolling a six-sided die, the sample space would consist of the outcomes {1, 2, 3, 4, 5, 6}. This set encompasses every possible result you could observe from that experiment. Recognizing the sample space is crucial for calculating probabilities accurately, as it outlines the context in which probabilities are defined.

In contrast, the other options refer to related but distinct concepts in the realm of probability. The total number of trials pertain to the frequency of experiments conducted, the average of all possible outcomes refers to statistical measures like the mean, and the most likely outcome addresses concepts such as mode in a distribution. However, none of these alternatives capture the essence of what a sample space represents in probability theory.