Given below are two statements : Statement I : When we perform an experiment,…
2020
Given below are two statements :
Statement I : When we perform an experiment, then the set S of all possible outcomes is called the sample space.
Statement II : Any superset of a sample space is called an event.
In the light of the above statements, choose the correct answer from the options given below :
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is correct but Statement II is false
- D.
Statement I is incorrect but Statement II is true
Attempted by 75 students.
Show answer & explanation
Correct answer: C
Complete Solution
To determine the validity of the statements, we evaluate them against standard probability definitions:
Evaluate Statement I: The definition provided—"the set S of all possible outcomes of an experiment is called the sample space"—is correct. In probability theory, the sample space consists of every possible outcome that can result from a random experiment.
Evaluate Statement II: An event is defined as any subset of the sample space, not a superset. A superset would include outcomes outside the possible results of the experiment, which contradicts the fundamental definition of an event. Therefore, this statement is false.
Conclusion: Statement I is true, and Statement II is false.