question_answer 1)

Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6. Find (i) P(A and B) (iii) P (A or B) (iii) P (A and not B) (iv) P (neither A nor B)  

Answer:

We have P(A) = 0.3, P(B) = 0.6 and A and B are independent events. Therefore,  are also independent events. (i)     P(A and B) = P(A  B)       (AB) = P(A) × P(B)       0.3 × 0.6 = 0.18 (ii)   P(A and not B) = P (A) = P(A) ×       = 0.3 × (1 ? 0.6) = 0.3 × 0.4 = 0.12 (iii)  P(A or B) = P(A  B) = 1 ? P                   = 1? P                                     = 1 ? 0.28 = 0.72 (iv)  P (neither A nor B) = 1 ? P(A or B)       = 1 ?0.72 = 0.28  {Using (iii)}