Consider two people each facing a lottery. One has a chance to Win a prize of $100 or go home with nothing. The other has a chance to win a prize of $10 or go home with nothing. In both cases the chance of winning depends on how many lottery tickets they earn from a task undertaken before the lottery. If x = the number of lottery tickets earned, the chance of winning a prize is i where x E [0,100]. Suppose both people are expected utility maximizers. Show that the preference of both can be represented by the same expected utility function. Exhibit that function