Question

If A and B are independent events, then A′ and B′ are also independent

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Given A and B are independent.

∴ P(A ∩ B) = P(A)·P(B)

P(A' ∩ B') = P(A' ∪ B')

= 1 – P(A ∪ B)

= 1 – [P(A) + P(B) – P(A ∩ B)]

= 1 – P(A) – P(B) – P(A)·P(B)

= (1 – P(A))(1 – P(B))

= P(A')P(B')

Thus A and B are also independent.