Question

If A and B are two events such that P(B) = `3/5`, P(A|B) = `1/2` and P(A ∪ B) = `4/5`, then P(A) equals ______.

पर्याय

• `3/10`

• `1/5`

• `1/2`

• `3/5`

Answer 1

If A and B are two events such that P(B) = `3/5`, P(A|B) = `1/2` and P(A ∪ B) = `4/5`, then P(A) equals `1/2`.

Explanation:

Given that: P(B) = `3/5`, P(A|B) = `1/2` and P(A ∪ B) = `4/5`

We know that P(A|B) = `("P"("A" ∩ "B"))/("P"("B"))`

⇒ `1/2 = ("P"("A" ∩ "B"))/(3/5)`

∴ P(A ∩ B) = `3/10`

Now  P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

`4/5 = "P"("A") + 3/5 - 3/10`

⇒ P(A) = `4/5 - 3/5 + 3/10`

= `1/5 + 3/10`

= `5/10`

= `1/2`