Sly asks Andy to play a game with him. They each roll a die. If the sum is greater than 7, Andy scores 5 points. If the sum is less than 8, Sly scores 4 points.
a. Find a friend and play the game ten times.
b. What is the experimental probability that Andy will have a higher score after ten games?
c. Draw a tree diagram of this situation showing the theoretical probabilities.
d. If you consider this game from Andy's point of view, his winning value is +5 and his losing value is −4. What is the expected value of the game from his point of view?
e. Suggest a different distribution of points that would favor neither player.