Eleven people have eleven different favorite numbers from 2 to 12. They all agree to participate in a 10,000-roll dice game where they bet$1 on their favorite number for each roll of two standard (fair) dice. A donor kicks in an extra dollar every round, so the payoff if your number comes up is $12.

a. Assuming everyone bets on all 10,000 rounds, what is the expected value for a person who has number 7?

b. Assuming everyone bets on all 10,000 rounds, what is the expected value for a person who has number 2? Show your calculations. Carefully, use parenthesis, brackets, etc. to make your calculations more legible.