Lotteries and expected utility. An expected utility maximizing decision maker declares that he prefers a lottery that pays $5 and $10 with equal probability to a lottery that pays $10 with probability 3 4 , and $0 with probability 1 4 . Which would the decision maker choose out of a lottery that pays $5 and $0 with equal probability, or a lottery that pays $10 with probability 1 4 and $0 with probability 3 4 ?