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.’

(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?

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Expert Solution

Colby Messinger answered 1 year ago

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