are) What is the protestality that the nutty isbeat the butt faves al and fate of Answer thing to boston exclusion principle, we have that - 0.53 + 065-08 -04 (h) rapes) Determine and interpret Petstates. Answers PlAlfAs in the probability that of a person person likmust flatter #2 given that that ( 10 ) putson likes flavor ed. The probability is given by 1)Hopes) Are As and A, independent events? Answers No, because "() - PC-tale D) (pts) Determine P(Asl4.) nattig Bayes rule, Answers thing Hayes' rule. we have that ( 17 ) - 0.613 ic) (4pts) What is the probability that the now Answer: We need to com " the Have ed and does not like flavor #a? Therefore. 1. (Set Theory and Axioms of Probability) (25 pts) (a) (10pts) Let events A, and As satisfy PIA,] - 1 and P[A,] - 1. Show that P[A, n A2] = 1 Instructions: For this question you are not allowed to use Venn diagrams. (b) (5pts) Suppose that P[A: ~ A,] - . Show that P[A2] > 2 Instructions: You are allowed to use any tools at your disposal. (c) (5pts) Suppose that P(A;] - P[A,] = ;, and A, and A2 are independent. Find P[A, U A2]. Instructions: Show all the steps. (d) (5 pts) Here need to justify by clearly showing your steps. In an experiment, A and B are independent events and we know that P[An B] = ; and PIA] = 1. Are A and B' mutually exclusive