Comme un jeu

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

and a blue die

. Construct the probability distribution table for \(M\).\FieldText{1}{The possible values of \(M\) are 1, 2, 3, 4, 5, 6. The probabilities are:

\(P(M = 1) = P(\{(1,1)\}) = \frac{1}{36}\),
\(P(M = 2) = P(\{(1,2), (2,1), (2,2)\}) = \frac{3}{36}\),
\(P(M = 3) = P(\{(1,3), (2,3), (3,1), (3,2), (3,3)\}) = \frac{5}{36}\),
\(P(M = 4) = P(\{(1,4), (2,4), (3,4), (4,1), (4,2), (4,3), (4,4)\}) = \frac{7}{36}\),
\(P(M = 5) = P(\{(1,5), (2,5), (3,5), (4,5), (5,1), (5,2), (5,3), (5,4), (5,5)\}) = \frac{9}{36}\),
\(P(M = 6) = P(\{(1,6), (2,6), (3,6), (4,6), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)\}) = \frac{11}{36}\).

\(m\)	1	2	3	4	5	6
\(P(M = m)\)	\(\frac{1}{36}\)	\(\frac{3}{36}\)	\(\frac{5}{36}\)	\(\frac{7}{36}\)	\(\frac{9}{36}\)	\(\frac{11}{36}\)

}