Consider the following game. A player rolls two dice. If the outcome on both dice is the same (doubles), the player wins $5. If the sum is 7 or 11, the player wins $3. If neither of these outcomes occurs, the player loses $1.

(a) Construct a decision tree to illustrate this game. Determine the expected payoff of the game.

(b) Construct a simulation of this game and simulate 10 games. Use random numbers from row 1 from the appropriate random number table.