Question

Two events, A and B, will be independent if ______.

Options

• A and B are mutually exclusive

• P(A′B′) = [1 – P(A)] [1 - P(B)]

• P(A) = P(B)

• P(A) + P(B) = 1

Answer 1

Two events, A and B, will be independent if P(A'B') = [1 − P(A)][1 - P(B)].

Explanation:

A and B are independent

⇒ P (A ∩ B) = P (A) P (B)

and 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))