This question pertains to the probability of rolling a giventotal (adding the two die face-values) using 2 fair 6-sided dice.The possible results of rolling 2 fair 6-sided dice are theelements of the Cartesian product A × A, where A = {1, 2, 3, 4, 5,6}.
(a) How many elements does A × A have?
(b) Partition the elements (x, y) of the set A × A according tothe sum x + y. For example, (1, 3) goes in the part labeled somehowby ‘4.’
(c) Write down all of the parts of the partition with all oftheir respective elements.
(d) Define an equivalence relation R on A × A so that theequivalence classes of R equal the parts of the partition in Part(c).
(e) Write down one representative of each equivalence class inthe equivalence relation R in Part (d).
(f) The most likely die total is |P|/|A × A|, where P is thelargest part of the partition you wrote down in Part (c). What isthe most likely die total?
