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

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

Answer: (A)

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 (or collection) of one or more outcomes. 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. Each event is made up of one or more outcomes grouped together based on some condition or property.
4. Step 4: Differentiate between the two by noting that an outcome is always a single result, while an event can be a single outcome or multiple outcomes combined.
5. Step 5: Summarize the main difference: an outcome is a single possible result of an experiment, whereas an event is a set of one or more such outcomes.