Problem 9.An urn contains five balls, two of which are marked $1, two $5, and one $15. The game is played as follows: You pay me $10 to select two balls at random (without replacement) from the urn, at which point I pay you the sum of the amounts marked on the two balls.

(a) Is this a fair game (meaning, is the cost of each turn equal to the expected payout)? Be precise and show all work.

(b) If your answer to (a) is "no," what should I charge for each turn to make it a fair game?