Chapter 9.3A, Problem 30A

Suppose you invented a game based on taking the sum of two dice. You decide the game will cost $\$5$ to play, with a play consisting of rolling the dice once, and taking the sum. If the person rolls a sum of $2$ or $12$, you will pay that person $\$20$. If the person rolls a sum of $3$ or $11$, you will pay that person $\$10$. If the person rolls a sum of $4$ or $10$, you will pay that person $\$7.50$. If the person rolls a sum of $5$ or $9$, you will pay that person $\$5$ (in other words, he or she wins the money back). If the person rolls a sum of $6,7$ or $8$, you will pay that person nothing.

a. What is the expected value?

b. Whom does the game favor?