The odds in rolling two dice together. Two dice are rolled. I want to see the odds of the following:
$1.$ A sum of $5$.
$2.$ A sum of $8$ or $10$.
$3.$ A sum less than $6$.
$4.$ Not a sum of $7$.

Solution: $1.$ A sum of $5$. $5 = 1+4,2+3,3+2,4+1$. So the odds is $4/36 = 1/9.$
$2.$ A sum of $8$ or $10$. We can express $8 = 2+6,3+5,4+4,5+3,6+2$ and $10 = 4+6,5+5,6+4$. So the odds is $8/36 = 2/9$.
$3.$ A sum less than $6$. We can express $2=1+1$, $3=1+2,2+1$, $4=1+3,2+2,3+1$ and $5 = 1+4,2+3,3+2,4+1$. So the odds is $10/36 = 5/18$.
$4.$ Not a sum of $7$. We can express $7 = 1+6,2+5,3+4,4+3,5+2,6+1$. So the odds is $\frac{36-6}{36} = \frac{30}{36} = \frac56$

Is the solution correct?

Yes, it states all of the ways the event can happen, then all of the possible events, yielding correct probability.
