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

Event \(E_1\): getting numbers less than 3 = \{1, 2\}
Event \(E_2\): getting numbers greater than 3 = \{4, 5, 6\} They are not complementary as they don't cover all possible outcomes. Complementary events together cover the entire sample space. Here, missing number 3. So, Assertion (A) is false. But Reason (R) is a true statement on complementary event property.