A) Suppose that Hye-mi starts with $100 and is offered a bet by Dae-du, one of her friends, that gives her a chance to win or lose $20 based on a draw from a deck of cards. Dae-du shuffles the deck and then Hye-mi cuts the deck. If she turns up a spade, then she wins. If she turns up a heart, diamond, or club, then she loses. [Reminder: There are 52 cards in a deck, 13 of each suit (club, spade, diamond, heart)). If Hye-mi wins the bet, then she will have .If she loses the bet, she will have $ Given these values, the expected utility of the bet to Hye-mi is Her expected utility from not taking the bet is so she compares these two expected values and take the bet from Dae-du.
b) Dae-du decides to make things a bit more interesting and offers Hye-mi a bigger bet. The same process is used (drawing a spade from the deck of cards wins), but this time the stakes are higher a $100 bet compared to the earlier $20 bet.
What is Hye-mi's expected utility from this bigger bet?
Is she willing to take the bet this time?