suppose you are playing a game that requires rolls of two 4-sided dice, which have sides numbered 1, 2, 3, and 4.
(a) if both dice are fair, then what is the probability distribution over the set of possible outcomes for the sum of the two dice, when rolled?
(b) now suppose that one die is weighted such that a 3 is twice as likely to be rolled as any other single number on that die, and 1, 2 and 4 are all equally likely to be rolled. what is the probability distribution for outcomes of a single roll of just that one loaded die?
(c) what is the probability that the total of the fair and unfair dice is 6, when both are rolled?
(d) suppose you roll both dice but one falls on the floor and rolls under the couch so you can’t see it, but the other die has rolled a 3. the unfair die is made of a strange material which makes it twice as likely as the fair die to fall off the table. without seeing the die that is under the couch, what is the probability that the dice total is 6?
(e) suppose these fair and unfair 4-sided dice, and two regular 6-sided dice are all in a bag. if you pick a die at random from the bag and roll it, what is the probability of rolling a 3?