ECON 4070 - Expected-utility theory tells us that a risk-averse individual

Expected-utility theory tells us that a risk-averse individual would want to be paid a risk premium to induce her to voluntarily accept risk. Or, alternatively, the riskaverse individual would have to be offered odds that were in her favor in order to induce her to gamble. Here, "odds" refer to the probability of loss/gain and/or the magnitude of the loss/gain.

Ms. Lee's utility function is U(Y) = (100 + Y) 0.5, where 100 is her initial income level and Y is additional income gained or lost from a gamble. Ms. Lee can choose not to gamble or to gamble. The gamble involves the roll of a fair dice. If the number is even Ms. Lee wins $100 but if it is odd Ms. Lee loses $100.

(i) Will Ms. Lee choose the gamble?

(ii) In words, briefly describe what would need to change to induce Ms. Lee to take the gamble (hint: focus on the characteristics of the gamble not her preferences).