Question

Directions: In Question Numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R).
Choose the correct option from the following:
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the 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.

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 the 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 all possible outcomes with no overlap or omission.

Answer 1

The Correct Option is D

On a die, numbers less than 3 = \{1, 2\}, greater than 3 = \{4, 5, 6\}. Total = 6 outcomes. But numbers equal to 3 (i.e., 3 itself) are not covered. So $E_1$ and $E_2$ are not complementary. Assertion is false.
However, Reason is correct: the probability of complementary events always sums to 1.