Consider the following card game with a well-shuffled deck of cards. If you draw a red card, you win nothing. If you get a spade, you win $5. For any club, you win $10 plus an extra $20 for the ace of clubs. Let the random variable X be the amount you win when you play this game. (a) What is the probability mass function of X? (b) Find E(X), the expected winnings. (c) What is the maximum amount you would be willing to pay to play this game?