Question

Let P(A) = `7/13`, P(B) = `9/13` and P(A ∩ B) = `4/13`. Then P( A′|B) is equal to ______.

Options

• `6/13`

• `4/13`

• `4/9`

• `5/9`

Answer 1

Let P(A) = `7/13`, P(B) = `9/13` and P(A ∩ B) = `4/13`. Then P( A′|B) is equal to `5/9`.

Explanation:

Given that: P(A) = `7/13`, P(B) = `9/13` and P(A ∩ B) = `4/13`

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

= `("P"("B") - "P"("A" ∩ "B"))/("P"("B"))`

= `(9/13 - 4/13)/(9/13)`

= `(5/13)/(9/13)`

= `5/9`