(Independence)

(a) Prove that P(A) = P(AB) + P(AB'). (B' is the complement of B)

(b) Prove that if A and B are independent, then so are A and B'.

(c) Prove that if A and B are independent, then so are A' and B'.

(Hint: use (a) to prove (b); (c) is a simply corollary of (b).)

(a) Prove that PiA) = PIAB-RAB) (B. is the complement of B) bProve bat if A B iepencz, ene A and B (c) Prove that ifA and B are indepeadent, then so areA andB Hint use (a) to prore (by: (e is a simply corollay af(b))