Problem 4. Use the axioms of a probability distribution to answer the following: (a) Describe a situation where we might have a sample space 2 such that P[{w} ] = 0 for all wen. (b) Explain what is wrong with the following proof that 1 = 0. Proof. By definition UwEn(w} = {w : 3w' E D with w e (w'}} = 2. Thus, 1 = P[2] (Axiom 2) = P Ulw} (definition of union) WED = ) P[(w} ] (Axiom 3) WEn E (assumption) WEL = 0