A Group of Participants Were Given the Following Gambles to Choose

A group of participants were given the following gambles to choose from: (a) winning $4000 with 80% chance and $0 with 20% chance OR (b) winning $3000 for sure. 80% of respondents chose gamble (b) over gamble (a). The same group of participants were then given a choice between (c) losing $4000 with 80% change and losing $0 with 20% chance OR (d) losing $3000 for sure. Now 92% of the participants choose gamble (c) over (d).
(a) Why do these choices represent an anomaly? What kind of preferences over gains and losses can explain this behaviour? (b) What do such preferences imply for the shape of the underlying value (utility) function? Draw a neat diagram to illustrate this value function. A neatly drawn diagram should be sufficient to answer this question. (c) On the diagram you drew for Part (b), show that the increase in value from a gain of a particular size is smaller than the increase in value from avoiding a loss of similar size. Either use coloured pencils or clearly mark (using letters A, B, C etc.) the relevant gains and losses on your diagram. Briefly explain your answer so that it is clear what you are showing on your diagram.