1.) Consider a following decision problem: You are at the dog-racing betting window. You may choose not to bet or you may bet on one of two dogs. Betting on Snoopy costs $1 and you get paid $2 if he wins. Betting on Lassie costs $1 and you get paid $11 if she wins. You believe that snoopy has probability 0.7 of winning, and that Lassie has probability of 0.1 of winning. There are other dogs racing on which you are not considering betting.
a) Draw the decision tree for this problem.
b) What is the best course of action and what is your expected payoff?
c) You are offered a gambler's "anti-insurance", which you may accept or decline. If you accept it, you get paid $2 up front and you agree to pay 50% of any winnings you receive. Draw the new decision tree and find the optimal action.