Why is the probability different? We launch two dice We launch two dice with faces $1 , 2, \dots, 6$, one black, one white.
I want to calculate the probability that the sum of the two dice's faces is $\geq 11$.
If I choose the main set as $\Omega = \{ (i,j) : i , j \in [[1,6]] \}$ we clearly have $|\Omega|  = 6^2 = 36$
and the only couples that give us the sum $\geq 11$ are $(6,5)$, $(5,6)$, $(6,6)$ so the probability is $3/36 = 1/12$.
Everything is good so far.
Now lets see if we take $\Omega$ as the set that contains the sums of the faces.
$\Omega = \{2,3 , \dots, 11, 12\}$ so $|\Omega|=11$.
So the probability that the sum of the two faces is $\geq 11$ is $2/11$ (either the sum is $11$ or $12$).
But $2/11 \neq 1/12$. What am I doing wrong here?

I forgot that the relation P=  Card(event)/Card(Omega) requires that the event set has a uniform probability (sorry for my english im french)
