The reference book I have used stating that: Axiom 1 stating that 0<=P(E)<=1 Axiom 2 stating that P(S)=1 Axiom 3, the probability of union of mutually exclusive events is equal to the summation probability of of each of the events. And the author says that, hopefully, the reader will agree that the axioms are natural and in accordance with our intuitive concept of probability as related to chance and randomness. But what if axiom 1 and axiom 2 is changed to Axiom 1 stating that 0.5<=P(E)<=1.5 Axiom 2 stating that P(S)=1.5 (Axiom 3 no change) or Axiom 1 stating that 1.1<=P(E)<=2 Axiom 2 stating that P(S)=2 (Axiom 3 no change) and rebuild the probability model base on the new axiom? Will there be any problem in this new probability model? If not can I say that the original Axiom 1 and Axiom 2 is just taking some reference value so everybody on the earth can follow it?