Question

If A and B are such events that P(A) > 0 and P(B) ≠ 1, then P(A′|B′) equals ______.

Options

• 1 – P(A|B)

• 1– P(A′|B)

• `(1 - "P"("A" ∪ "B"))/("P"("B'"))`

• P(A′)|P(B′)

Answer 1

If A and B are such events that P(A) > 0 and P(B) ≠ 1, then P(A′|B′) equals `(1 - "P"("A" ∪ "B"))/("P"("B'"))`.

Explanation:

Given that: P(A) > 0 and P(B) ≠ 1

∴ P(A′|B′) = `("P"("A'" ∩ "B'"))/("P"("B'"))`

= `(1 - "P"("A" ∪ "B"))/("P"("B'"))`