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Question
If P(A) = `3/10`, P(B) = `2/5` and P(A ∪ B) = `3/5`, then P(B|A) + P(A|B) equals ______.
Options
`1/4`
`1/3`
`5/12`
`7/12`
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Solution
If P(A) = `3/10`, P(B) = `2/5` and P(A ∪ B) = `3/5`, then P(B|A) + P(A|B) equals `7/12`.
Explanation:
Here, P(A) = `3/10`, P(B) = `2/5` and P(A ∪ B) = `3/5`
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
⇒ `3/5 = 3/10 + 2/5` – P(A ∩ B)
⇒ P(A ∩ B) = `3/10 + 2/5 - 3/5`
= `(3 + 4 - 6)/10`
= `1/10`
Now `"P"("A"/"B") + "P"("B"/"A") = ("P"("A" ∩ "B"))/("P"("B")) + ("P"("A" ∩ "B"))/("P"("A"))`
= `(1/10)/(2/5) + (1/10)/(3/10)`
= `1/4 + 1/3`
= `7/12`
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