Question

In an experiment of throwing a die,

Assertion (A):

Event E₁: Getting a number less than 3.

Event E₂: 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

Options

• Both Assertion (A) and Reason (R) are true, and Reason (R) is a correct explanation of Assertion (A).

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

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

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

Explanation:

S = {1, 2, 3, 4, 5, 6}

E₁ = {1, 2}

E₂ = {4, 5, 6}

P(E₁) = `2/6`

P(E₂) = `3/6`

P(E₁) + P(E₂) ≠ 1

E₁​ and E₂​ are not complementary events.

So, Assertion (A) is false.

For any two complementary events E and F,

P(E) + P(F) = 1

Hence, Reason (R) is true.