Suppose you are asked to play a game where you roll a single six-sided die. If it lands on a 6, you win $10. If it doesn’t land on 6, you roll again. If it lands on a 6, the second time you win $6. For any other outcome, you lose. Let X be the amount of money you win. 

a. Create a probability distribution for X. 

b. What is the expected value for this distribution? What does this expected value mean? 

c. How much money would you have to pay to play this game for it to be a fair game? (A fair game is when the expected value of winning is zero.)