You have the chance to play the following game in a gambling casino. A fair die is rolled twice, leading to four outcomes: 

(1) Both rolls show the same even number, 

(2) Both rolls show the same odd number, 

(3) The two rolls show either even followed by odd or odd followed by even, and 

(4) All other outcomes. You are allowed to bet your money on exactly two outcomes with equal dollar amounts. For example, you can bet equal dollars on even-match (outcome 1) and odd-match ( outcome 2). The payoff for each dollar you bet is $2.00 for the first outcome, $1.95 for the second and the third outcomes, and $1.50 for the fourth outcome.

(a) Draw the decision tree for the game.

(b) Which two choices would you make?

(c) Do you ever come out ahead in this game?