Question 2. [25 marks] Regina is participating in an experiment in which she will be asked to make bets based on draws of balls from urns. For the first task, she is told there are 100 hundred balls in an urn: 33 are red, m are black and the remaining 67-m are yellow. The only information she is given about m is that it is at least 1 and at most 66. She is asked which of the three colors red, black or yellow does she want to bet on. She wins $20 if the color of the ball drawn from the urn matches the color she has chosen. She wins nothing if it doesn't. As Regina prefers to win $20 over not winning anything, she ranks bets on the basis of the weight she assigns to the event that a bet will win. Assume Regina believes it is equally likely any of the 100 balls will be drawn from this urn. She chooses to bet on red. (a) [5 marks] Show that her preferences over bets cannot conform to subjective expected utility theory