Question

If A and B are two events such that P(A|B) = p, P(A) = p, P(B) = `1/3` and P(A ∪ B) = `5/9`, then p = ______.

Answer 1

If A and B are two events such that P(A|B) = p, P(A) = p, P(B) = `1/3` and P(A ∪ B) = `5/9`, then p = `1/3`.

Explanation:

Given that, P(A) = p

P(B) = `1/3`

And P(A ∪ B) = `5/9`

P(A|B) = `("P"("A" ∩ "B"))/("P"("B"))` = p

⇒ P(A ∩ B) = p

P(B) = `"p"*1/3` and P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

`5/9 = "p" + 1/3 - "p"/3`

⇒ `5/9 - 1/3 = (2"p")/3`

⇒ `2/9 = (2"p")/3`

⇒ p = `1/3`