Question

If A and B are any two events such that P (A) + P (B) − P (A and B) = P (A), then ______.

Options

• P (B|A) = 1

• P (A|B) = 1

• P (B|A) = 0

• P (A|B) = 0

Answer 1

If A and B are any two events such that P (A) + P (B) − P (A and B) = P (A), then P(A|B) = 1.

Explanation:

P(A) + P(B) – P(A ∩ B) = P(A)

⇒ P(B) − P(A ∩ B) = 0

P(A ∩ B) = P(B)

or `(P(A ∩ B))/(P(B))` = 1

P(A|B) = 1