2. Let O be a sample space. The axioms of probability are: Axiom 1 P (A) 0, for all events A O. Axiom 2 P(Q) = 1. Axiom 3 If events A and B satisfy A B = then P (A IJ B) = P(A) -F P (B). (a) For events A and B, prove that (b) For events A, B and C, prove that U B U C) = P(A) + P(B) + P(C) - n B) - P(AFIC) - n C) + POI n B n C).