This question pertains to the probability of rolling a given total (adding the two die face-values)...

This question pertains to the probability of rolling a given total (adding the two die face-values) using 2 fair 6-sided dice. The possible results of rolling 2 fair 6-sided dice are the elements 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 to the sum x + y. For example, (1, 3) goes in the part labeled somehow by ‘4.’

(c) Write down all of the parts of the partition with all of their respective elements.

(d) Define an equivalence relation R on A × A so that the equivalence classes of R equal the parts of the partition in Part (c).

(e) Write down one representative of each equivalence class in the equivalence relation R in Part (d).

(f) The most likely die total is |P|/|A × A|, where P is the largest part of the partition you wrote down in Part (c). What is the most likely die total?

Expert Solution

Colby Messinger answered 1 year ago

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