Question

A subset of the sample space associated with a random experiment, is called an

• A. Event
• B. Probability
• C. Sample Space
• D. Determinant

Hint:

Remember the basic hierarchy of probability terms:
$\text{Random Experiment} \rightarrow \text{All Outcomes (Sample Space)} \rightarrow \text{Subset of Outcomes (Event)} \rightarrow \text{Likelihood of Subset (Probability)}$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Probability theory provides a mathematical framework for analyzing random experiments, where the exact outcome cannot be predicted with certainty.
Defining terms like sample space, outcomes, and events is essential for building and applying probability models.

Step 2: Detailed Explanation:
Let us review the definitions of each term:
1. Sample Space (S): The set of all possible outcomes of a random experiment.
For example, rolling a six-sided die has the sample space $S = \{1, 2, 3, 4, 5, 6\}$.
2. Event (E): Any subset of this sample space.
An event can consist of a single outcome (elementary event) or multiple outcomes (compound event).
For example, the event "rolling an even number" is the subset $E = \{2, 4, 6\}$, which is a subset of the sample space $S$.
This matches the definition provided in the question.
3. Probability: A numerical measure of the likelihood that a specific event will occur, ranging from $0$ to $1$.
4. Determinant: A mathematical value calculated from a square matrix, unrelated to probability.

Step 3: Final Answer:
A subset of a sample space is defined as an event.
Hence, the correct option is (A).