Consider the following experiment that involves asking a person two questions. Question 1: Choose between two lotteries:

A. Win $6000 with 80% chance and win nothing with 20% chance;

B.Win $3000 with certainty. Question 2: Choose between two lotteries:

C. Win $6000 with 20% chance and win nothing with 80% chance;

D.Win $3000 with 25% chance and win nothing with 75% chance. Suppose 100 people were asked with these two questions.

For Question 1, 20 people chose A and 80 chose B;

For Question 2, 65 chose C and 35 chose D. So at least 80% 65% = 52% people preferred B over A and at the same time preferred C over D. Show that this preference relation cannot be represented by any utility function that has the expected utility property.