A zero-sum game (also known as a strictly competitive game) is one in which the player's expected gain is zero. That is, if W is a random variable representing the

player's gain (or "winnings"), then a zero-sum game has E[W] = 0.Problem 6(Zero-sum game) (a) (5 points) Suppose your friend offers to play the following game with you: You roll the seven-sided die from Problem 5. If you get a 1, your friend will give you $50.00. If you roll a -4, your friend will give you $20.00. If you roll a 3, you must give your friend$250.00. Calculate the expected value of your winnings. Is this game worth playing? (b) (2 points) Do you think that casino games are zero-sum games? Explain.