(i) P(A and B) = P (A ∩ B) = P(A) × P(B) (Q A and B are independent,
⇒ P(A ∩ B) = 0.3 × 0.6 = 0.18
(ii) P(A and not B) =P(A∩Bc)=P(A)×P(Bc)
(∵ A and B are independent ∴ A and Bc are also independent)
= (0.3)(1– P(B)) = (0.3)(1 – 0.6) = (0.3) (0.4) = 0.12.
(iii) P(A or B) = P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
⇒ P(A ∪ B) = P(A) + P(B) – P(A) P(B) (∵ A and B are independent)
= 0.3 + 0.6 – 0.3 × 0.6 = 0.9 – 0.18 = 0.72.
(iv) P(neither A nor B) = P(Ac‌and‌Bc) =P(Ac∩Bc) =P((A∪B)c) =1−P(A∪B) = 1 – 0.72 = 0.28 (using part (iii))