Question

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

Answer 1

We have P(A) = `1/2`

P(B) = `1/3` 

And P(A ∩ B) = `1/4`

P(A') = `1 - 1/2 = 1/2`

P(B') = `1 - 1/3 = 2/3`

P(A' ∩ B') = 1 – P(A ∪ B)

= 1 – [P(A) + P(B) – P(A ∩ B)]

= `1 - [1/2 + 1/3 - 1/4]`

= `1 - [(6 + 4 + 3)/12]`

= `1 - 7/12`

= `5/12`

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

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

= `1 - ("P"("A" ∩ "B"))/("P"("B"))`

= `1 - (1/4)/(1/3)`

= `1 - 3/4`

= `1/4`