Question

In an experiment of throwing a die, Assertion (A): Event \(E_1\): getting a number less than 3 and Event \(E_2\): getting a number greater than 3 are complementary events. Reason (R): If two events E and F are complementary events, then \(P(E) + P(F) = 1\).

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Hint:

Complementary events together cover the entire sample space.

Answer 1

The Correct Option is C

Given:
- Assertion (A): Event \(E_1\) is a number less than 3.
- Event \(E_2\) is a number greater than 3.
- Reason (R): If events \(E\) and \(F\) are complementary, \(P(E) + P(F) = 1\).

Step 1: Analyze Assertion (A)
- \(E_1\) = numbers less than 3 → \{1, 2\}
- \(E_2\) = numbers greater than 3 → \{4, 5, 6\}
- The events don't include all possible outcomes (missing 3).
Therefore, \(E_1\) and \(E_2\) are not complementary.

Step 2: Analyze Reason (R)
- The statement about complementary events is correct: for complementary events \(E\) and \(F\), \(P(E) + P(F) = 1\).

Conclusion:
- Assertion (A) is valid because it accurately describes the events.
- Reason (R) is invalid because \(E_1\) and \(E_2\) are not complementary.

Final Answer:
Assertion (A) is true, but Reason (R) is false.