Question 4: There are three alternatives X E {931,132,273}, and Ann's preference on the lotteries over X has an expected utility representation. Her vNM utility function is given by: o 15(181) = 3, 11.0132) = 1, 11(13): 2. Now answer the following questions: 1. How would Ann choose between lottery A and lottery B? Lottery A: alternative :51 with probability 1/4, alternative 1:2 with probability 1/2, alternative 2:3 with probability 1/4. Lottery B: alternative 2:1 with probability 1/8, alternative 3:2 with probability 2/3, alternative 2:3 with probability 5/24. 2. Consider another vNM utility function 1:, with ohm) = 10, 0(32) = 5 and 12(333) = 8. Do 1: and 1:. represent the same preference over lotteries? If yes, explain why. If no, construct a pair of lotteries such that the preference according to o and the preference according to a differ. 3. Consider another vNM utility function to, with w(:1:1) = 20, 10(132) = 10 and w(:t:3) = 15. Do to and 11. represent the same preference over lotteries? If yes, explain why. If no, construct a pair of lotteries such that the preference according to w and the preference according to a differ