What is the probablity that the sum of two dice is 4 or 6? 
What is the probablity that the sum of two dice is 4 or 6?

The explanation I found is as follows:
Total number of outcomes $6 \times6 = 36$
Number of outcomes where the event occurs: $1+3, 2+2, 3+1, 1+5, 2+4, 3+3, 4+2$ and $5+1$ (Total $ 8$)
The probability that the event occurs is $8/36$ or $2/9$
My doubt is why $1+3$ and $3+1$ are considered as separate outcomes. Isn't it the same as the dices are identical and we cannot really find out which dice had which number on it?

Here is a simple way to visualize the sample space:
\begin{array}{c|llllll}
+ & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
1 & 2 & 3 & \color{blue}{4} & 5 & \color{blue}{6} & 7\\
2 & 3 & \color{blue}{4} & 5 & \color{blue}{6} & 7 & 8\\
3 & \color{blue}{4} & 5 & \color{blue}{6} & 7 & 8 & 9\\
4 & 5 & \color{blue}{6} & 7 & 8 & 9 & 10\\
5 & \color{blue}{6} & 7 & 8 & 9 & 10& 11\\
6 & 7 & 8 & 9 & 10& 11 & 12\\
\end{array}
In blue we have the favourable outcomes.  Hence, the probability of getting a sum of $4$ or $6$ is $8/36$, or $2/9$, as desired.
