You are playing a game that involves rolling two dice (number cubes) numbered 1, 2, 4, 5, 5, 6.

Part A:
If the score for one roll of the game is the sum of the two numbers on the dice, what is the expected value? Show all your work including your table and the sum of the outcomes! Express your answer as a simplified improper fraction, mixed number, or decimal to 4 places.

Part B:
If the score for one roll of the dice is the PRODUCT of the two numbers on the dice, what are the smallest and largest possible outcomes? What is the expected value? Show all your work including your table and the sum of the outcomes!

Part C:
The rules of the game are altered so that the number of points you score is the product of the two dice unless you roll doubles in which case you lose the product. For example, if you roll a 3 and a 5 you gain 15 points, but if you roll two 4’s you lose 4*4=16 points. What is the expected value for one turn. Show all your work!