1. In role-playing games, different dice are used for different character actions. For dealing damage with a particular weapon in the game, a player rolls an eight-sided die (d8). On a critical hit, the number of damage dice rolled is doubled. Suppose X1 and X2 represent the die results of a critical hit dam- age roll with the weapon. Find the probability function for X1 + X2, the total amount of critical hit damage dealt by the player using the weapon.

2. Pop quiz! Cora is surprised by a pop quiz 15 questions long in a class. Each question has four possible answers, and no question depends on the answer to another. Cora decides to guess her way through the quiz. Using random variables, write expressions for the following probabilities and solve them with R.

(a) The probability that Cora gets exactly 4 questions right.

(b) That probability that Cora gets at most 8 questions right. (c) The probability that Cora gets between 3 and 10 questions right.