You are in possession of an unusual 5-sided die. Specifically, the die, which is not evenly weighted, takes on five different values with the following probabilities for each roll: 3 with probability 1/3; 4 with probability ¼; 5 with probability 1/5; 6 with probability 1/6; 20 with probability 1/20 Now suppose that you and your friend play the following game: In each round, you roll a die. If you roll a 4 or 20, your friend gives you a dollar. If you roll a 3, 5, or 6, you give you friend a dollar. A game consists of ten such rounds.
a. What is the probability that you come out even of win money after playing just one game?
b. What is the expected monetary gain or loss to you for playing this game?