Assume an agent prefers $20 for sure than a lottery that pays $100 with probability 1/4

and $0 with probability 3/4. Also suppose that the agent prefers lottery A to lottery B,

where lottery A pays $100 with probability 1/8 and $0 with probability 7/8, and lottery B

pays $20 with probability 1/2 and $0 with probability 1/2. Is there a vNM utility function

that is consistent with his preferences? If so, describe such a utility function. Otherwise,

explain why not.