Comme un jeu

Let \(D\) represent the absolute difference of the numbers obtained when rolling two fair six-sided dice: a red die

and a blue die

. Construct the probability distribution table for \(D\).\FieldText{1}{The possible values of \(D\) are 0, 1, 2, 3, 4, 5. The probabilities are:

\(P(D = 0) = P(\{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\}) = \frac{6}{36}\),
\(P(D = 1) = P(\{(1,2), (2,1), (2,3), (3,2), (3,4), (4,3), (4,5), (5,4), (5,6), (6,5)\}) = \frac{10}{36}\),
\(P(D = 2) = P(\{(1,3), (2,4), (3,1), (3,5), (4,2), (4,6), (5,3), (6,4)\}) = \frac{8}{36}\),
\(P(D = 3) = P(\{(1,4), (2,5), (3,6), (4,1), (5,2), (6,3)\}) = \frac{6}{36}\),
\(P(D = 4) = P(\{(1,5), (2,6), (5,1), (6,2)\}) = \frac{4}{36}\),
\(P(D = 5) = P(\{(1,6), (6,1)\}) = \frac{2}{36}\).

Complete the table:

\(d\)	0	1	2	3	4	5
\(P(D = d)\)	\(\frac{6}{36}\)	\(\frac{10}{36}\)	\(\frac{8}{36}\)	\(\frac{6}{36}\)	\(\frac{4}{36}\)	\(\frac{2}{36}\)

}