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Question
Solve the following:
If P(A) = `"P"("A"/"B") = 1/5, "P"("B"/"A") = 1/3` the find `"P"("A'"/"B")`
Solution
Since P(A) = `"P"("A"/"B") = 1/5`,
P(A) = `1/5 and ("P"("A" ∩ "B"))/("P"("B")) = 1/5`
∴ P(A) = `1/5` ...(i)
P(B) = 5P(A ∩ B) ...(ii)
Since `"P"("B"/"A") = 1/3`,
`("P"("A" ∩ "B"))/("P"("A")) =1/3`
∴ P(A) = 3P(A ∩ B) ...(iii)
`"P"("A'"/"B") = ("P"("A'"∩ "B"))/("P"("B")`
= `("P"("B") - "P"("A" ∩ "B"))/("P"("B")`
= `1 - ("P"("A" ∩ "B"))/("P"("B"))`
= `1 - 1/5` ...[From (ii)]
= `4/5`.
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