At the Dog Races: You’re in Las Vegas, and you must decide what to do at the dog-racing betting window. You may choose not to participate or you may bet on one of two dogs as follows. Betting on Snoopy costs $1, and you will be paid $2 if he wins. Betting on Lassie costs $1, and you will be paid $11 if she wins. You believe that Snoopy has probability 0.7 of winning and that Lassie has probability 0.1 of winning (there are other dogs on which you are not considering betting). Your goal is to maximize the expected monetary return of your action.
a. Draw the decision tree for this problem.
b. What is your best course of action, and what is your expected value?
c. Someone offers you gambler’s “anti-insurance,” which you may accept or decline. If you accept it, you get paid $2 upfront and you agree to pay back 50% of any winnings you receive. Draw the new decision tree and find the optimal action.
