In the following question, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): If a dice is thrown the probability of getting a number less than 3 and greater than 2 is zero.
Reason (R): Probability of an impossible event is zero.

Options

A. Both A and R are true and R is the correct explanation for A.
B. Both A and R are true and R is not correct explanation for A.
C. A is true but R is false.
D. A is false but R is true.

Answer

To solve the problem, we need to analyze the assertion (A) and the reason (R) given in the question.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that if a die is thrown, the probability of getting a number that is both less than 3 and greater than 2 is zero.
- The numbers on a standard die are 1, 2, 3, 4, 5, and 6.

2. **Identifying Numbers Less Than 3**:
- The numbers less than 3 are: 1, 2.
- Therefore, the set of numbers less than 3 is {1, 2}.

3. **Identifying Numbers Greater Than 2**:
- The numbers greater than 2 are: 3, 4, 5, 6.
- Therefore, the set of numbers greater than 2 is {3, 4, 5, 6}.

4. **Finding Common Elements**:
- Now, we need to find the common elements between the two sets:
- Less than 3: {1, 2}
- Greater than 2: {3, 4, 5, 6}
- There are no common elements between these two sets.

5. **Conclusion About the Event**:
- Since there are no numbers that are both less than 3 and greater than 2, this event is impossible.
- Therefore, the probability of this event occurring is zero.

6. **Understanding the Reason (R)**:
- The reason states that the probability of an impossible event is zero.
- This is a true statement in probability theory.

7. **Final Evaluation**:
- Both the assertion (A) and the reason (R) are true.
- Additionally, the reason correctly explains the assertion.
- Thus, the correct choice is that both the assertion and reason are true, and the reason is the correct explanation of the assertion.

### Final Answer:
Both Assertion (A) and Reason (R) are true, and the reason is the correct explanation of the assertion.

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