Question

Assertion (A) A subset of a sample space is associated with an event and an event is associated with a subset of sample space.
Reason (R) Any subset $E$ of a sample space $S$ is called an event.

• A. Both $\triangle$ and $R$ are correct; $R$ is the correct explanation of $\triangle$
• B. Both A and R are correct; $R$ is not the correct explanation of $A$
• C. $A$ is correct, $R$ is incorrect
• D. $R$ is correct; $A$ is incorrect

Answer 1

Answer: (B)

We have studied about random experiment and sample space associated with an experiment. The sample space serves as an universal set for all questions concerned with the experiment.
Consider the experiment of tossing a coin two times. An associated sample space is $S=\{H H, H T, T H, T T\}$.
Now, suppose that we are interested in those outcomes which correspond to the occurrence of exactly one head. We find that $H T$ and $T H$ are the only elements of $S$ corresponding to the occurrence of this happening (event). These two elements form the set $E=\{H T, T H\}$.
We know that, the set $E$ is a subset of the sample space $S$. Similarly, we find the following correspondence between events and subsets of $S$.

The above discussion suggests that a subset of sample space is associated with an event and an event is associated with a subset of sample space. In the light of this, we define an event as follows
Any subset $E$ of a sample space $S$ is called an event.