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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`
Solution
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`
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