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`

Answer 1

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`