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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")`
Solution
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`
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