Sum

Solve the following:

If P(A) = `"P"("A"/"B") = 1/5, "P"("B"/"A") = 1/3` the find `"P"("A"/"B")`

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#### 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`.

Concept: Independent Events

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