$7.$ Suppose that the point spread for a particular sporting event is $10$ points and that with this spread you are convinced you would have a $0\mathrm{.}60$ probability of winning a bet on your team. However, the local bookie will accept only a $$1000$ bet. Assuming that such bets are legal, would you bet on your team? $($Disregard any commission charged by the bookie.$)$ Remember that you must pay losses out of your own pocket. Your payoff table is as follows: $182$ Chapter $5$ Utility and Game Theory State of Nature Decision Alternatives You Win You Lose Bet $$1000$ $$1000$ Don$$t bet $$0$ $$0$

a$.$ What decision does the expected value approach recommend?

b$.$ What is your indifference probability for the $$0$ payoff? $($Although this choice isn$$t easy, be as realistic as possible. It is required for an analysis that reflects your attitude toward risk.$)$

c$.$ What decision would you make based on the expected utility approach? In this case are you a risk taker or a risk avoider?

d$.$ Would other individuals assess the same utility values you do$?$ Explain.

e$.$ If your decision in part $($c$)$ was to place the bet, repeat the analysis assuming a minimum bet of $$10,000.$