Question

Let A and B be two events such that `P(A) = 1/2, P(B) = p` and `P(A ∪ B) = 3/5` find ‘p’ if A and B are independent events.

Answer 1

Given: `P(A) = 1/2, P(B) = p` and `P(A ∪ B) = 3/5`.

We know, P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

⇒ `3/5 = 1/2 + p - P(A ∩ B)`

⇒ `P(A ∩ B) = 1/2 - 3/5 + p`

= `p + 1/2 - 3/5`

= `p + (5 - 6)/10`

= `p - 1/10`

Now, A and B are independent events.

∴ P(A ∩ B) = P(A) × P(B)

⇒ `p - 1/10 = 1/2 xx p`

⇒ `p - p/2 = 1/10`

⇒ `p/2 = 1/10`

∴ `p = 2/10 = 1/5`