1.) [2 points] Based on your simulation, do you think that the casino should offer this game? Explain why or why not.

2.) Another way to approach this problem is to use theoretical probability. a. [3 points] Write out the sample space for rolling two dice. There should be a total of 36 possible outcomes.

b. [4 points] Using your sample space from part a, circle all of the outcomes where the player wins (the difference of the dice was two.). What is the probability that the player wins? What is the probability the player loses (casino wins)?

c. [4 points] Using part b, compute the expected value of this game to the player using the theoretical probability. Round your answer to two decimal places.

d. [3 points] Interpret the expected value of this game to the player. Using this interpretation, do you think the casino should continue offering this game? Explain why or why not.

3.) [3 point] Does your empirical average win/loss per game match your theoretical expected value? Should these values match? Explain why or why not.

4.) [2 points] How could the casino change the winning amount to make this into a fair game (where neither the player nor the casino have an expected value advantage?)