Question

If A and B′ are independent events, then P(A' ∪ B) = 1 – P (A) P(B')

Options

• True

• False

Answer 1

This statement is True.

Explanation:

P(A' ∪ B') = P(A') + P(B) – P(A' ∩ B)

= P(A') + P(B) – [P(B) – P(A ∩ B)]

= 1 – P(A) + P(B) – P(B) – P(A)P(B)

= 1 – P(A) – P(A)P(B)

= 1 – P(A)(1 – P(B))

= 1 – P(A)P(B')