In probability theory, what is the main difference between an $\mathrm{outcome}$ and an $\mathrm{event}$?

• A. An $\mathrm{outcome}$ is a set of possible results, while an $\mathrm{event}$ is always a single result.
• B. An $\mathrm{outcome}$ and an $\mathrm{event}$ are always the same in probability theory.
• C. An $\mathrm{outcome}$ refers to the probability of an $\mathrm{event}$, while an $\mathrm{event}$ is the process of conducting an experiment.
• D. An $\mathrm{outcome}$ is a single possible result of an experiment, while an $\mathrm{event}$ is a set of one or more $\mathrm{outcome}s$.

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the definition of an outcome in probability theory. An outcome is a single possible result of a random experiment. For example, when rolling a die, an outcome could be rolling a 3.
2. Step 2: Understand the definition of an event. An event is a set of one or more outcomes. It can include multiple outcomes or just a single outcome. For example, the event 'rolling an even number' includes the outcomes {2, 4, 6}.
3. Step 3: Recognize that outcomes are the basic building blocks of events. Events are formed by grouping outcomes together based on some condition or property.
4. Step 4: Note that the probability of an event is the sum of the probabilities of the outcomes that make up that event.
5. Step 5: Summarize the main difference: an outcome is a single possible result, while an event is a collection (set) of one or more such outcomes.