Question

Let A and B be two events such that 0 < P(A) < 1 and 0 < P(B) < 1. Then which one of the following statements is NOT true ?

• A. If A(A|B) > P(A), then P(B|A) > P(B)
• B. If P(A ∪ B) = 1, then A and B cannot be independent
• C. If P(A|B) > P(A), then P(Ac|B) < P(Ac)
• D. If P(A|B) > P(A), then P(Ac|Bc) < P(Ac)

Answer 1

Answer: (D)

If P(A|B) > P(A), then P(Ac|Bc) < P(Ac)

Answer 2

The correct option is (D) : If P(A|B) > P(A), then P(Ac|Bc) < P(Ac).