s (to be solved and submitted using the latex template provided). This problem set will refer to a standard deck of cards. Each card in such a deck has a rank and a suit. The 13 ranks, ordered from lowest to highest, are 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace. The 4 suits are clubs (), diamonds (), hearts (), and spades (). Cards with clubs or spades are black, while cards with diamonds or hearts are red. The deck has exactly one card for each rank-suit pair: 4 of diamonds, queen of spades, etc., for a total of 13 4 = 52 cards. 1. [10 pts] Suppose you roll three fair six-sided dice and add up the numbers you get. What is the probability that the sum is at most 6? Begin by clearly defining the probability space in which you work. 2. [10 pts] Prove that if A and B are events, then Pr[A B] Pr[A] + Pr[B] 1