Suppose you are playing a game that requires rolls of two 4-sided dice, which have sides numbered 1, 2, 3, and 4.

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 di