Question

If A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A/B) = `1/4`, P(A' ∩ B') equals ______.

Options

• `1/12`

• `3/4`

• `1/4`

• `3/16`

Answer 1

If A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A/B) = `1/4`, P(A' ∩ B') equals `1/4`.

Explanation:

Given that: P(A) = `1/2`, P(B) = `1/3` and P(A/B) = `1/4`

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

`1/4 = ("P"("A" ∩ "B"))/(1/3)`

⇒ P(A ∩ B) = `1/4 xx 1/3 = 1/12`

Now P(A' ∩ B') = 1 – P(A ∪ B)

= 1 – [P(A) + P(B) – P(A ∩ B)]

= `1 - [1/2 + 1/3 - 1/12]`

= `1 - [5/6 - 1/12]`

= `1 - 9/12`

= `3/12`

= `1/4`