1. Let 5] be a sample space. The axioms of probability are: Axiom 1 P(A) 2 I], for all events A Q Q. Axiom 2 13(9) = 1. Axiom 3 If events A and B satisfy .4 DB 2 , then P(A U B} 2 Put) + 13(3). Let A, B Q Q be events. (a) Prove that P(A'} = 1 PTA}. (b) Preve that if A g B then PTA) 5 P(B). [7]