Question

If A and B are two events such that `P(A) = 1/4, P(B) = 1/2 and P(A ∩ B) = 1/8`, find P (not A and not B).

Answer 1

As `P (A cap B) = 1/8 = 1/4 xx 1/2 = P (A) xx P (B)`

⇒ A and B are independent.

⇒ A^c and B^c are also independent.

⇒ P (A^c ∩ B^c) = P (A^c) P (B^c)

⇒ P (A^c ∩ B^c) = (1 - P(A)) (1 - P (B))

`= (1 - 1/4) (1 - 1/2) = 3/4 xx 1/2 = 3/8`

(∴ P (A^c) = 1 - P (A) & P(B^c) = 1 - P (B))