Question

Given two independent events A and B such that P (A) = 0.3, P (B) = 0.6. Find 

(i) P (A and B)

(ii) P (A and not B)

(iii) P (A or B)

(iv) P (neither A nor B)

Answer 1

(i)  i.e. P (A∩B) = P (A) x P (B) 

= .3 x .6 = .18 

(ii) P(A and not B) = = P(A) x 

⇒ P (A) x [1-P(B)] = .3 x (1 – 0.6) = .3 x .4 = .12 

(iii)  P(A or B) = P(A∪ B) = P(A) + P(B) – P(A∩B) = .3+ .6-.18 = .9 -.18 = .72 

(iv)  P(neither A nor B)