Question

Let A and B be two events such that P(A) = 0.6, P(B) = 0.2, and P(A|B) = 0.5. Then P(A′|B′) equals ______.

Options

• `1/10`

• `3/10`

• `3/8`

• `6/7`

Answer 1

Let A and B be two events such that P(A) = 0.6, P(B) = 0.2, and P(A|B) = 0.5. Then P(A′|B′) equals `3/8`.

Explanation:

P(A ∩ B) = P(A|B) P(B)

= 0.5 × 0.2

= 0.1

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

= `("P"[("A" ∪ "B")])/("P"("B'"))`

= `(1 - "P"("A" ∪ "B"))/(1 - "P"("B"))`

= `(1 - "P"("A") - "P"("B") + "P"("A" ∩ "B"))/(1 - 0.2)`

= `3/8`.