1. Total possible outcomes

Each die has 6 faces labeled: $\{1,2,3,5,7,11\}$

When two dice are rolled, total number of equally likely ordered outcomes is: $6 \times 6 = 36$

2. We need outcomes with sum $\le 8$

Let us count favorable ordered pairs $(a,b)$ where $a+b \le 8$ with $a,b \in \{1,2,3,5,7,11\}$.

We check each possible value on the first die.

• If first die shows $1$, then second die can be: $1,2,3,5,7$ since $1+1=2,\;1+2=3,\;1+3=4,\;1+5=6,\;1+7=8$ but $1+11=12>8$ So, favorable outcomes = $5$.

• If first die shows $2$, then second die can be: $1,2,3,5$ since $2+1=3,\;2+2=4,\;2+3=5,\;2+5=7$ but $2+7=9>8,\;2+11=13>8$ So, favorable outcomes = $4$.

• If first die shows $3$, then second die can be: $1,2,3,5$ since $3+1=4,\;3+2=5,\;3+3=6,\;3+5=8$ but $3+7=10>8,\;3+11=14>8$ So, favorable outcomes = $4$.

• If first die shows $5$, then second die can be: $1,2,3$ since $5+1=6,\;5+2=7,\;5+3=8$ but $5+5=10>8$ So, favorable outcomes = $3$.

• If first die shows $7$, then second die can be: $1$ since $7+1=8$ but all others give sum greater than $8$. So, favorable outcomes = $1$.

• If first die shows $11$, then no value on second die works, because $11+1=12>8$ So, favorable outcomes = $0$.

3. Total favorable outcomes

$5+4+4+3+1+0=17$

4. Probability

$P(\text{sum} \le 8)=\frac{17}{36}$

5. Compare with options

The probability is $\boxed{\frac{17}{36}}$ which is Option D.

6. Comparison with stored correct answer

Stored correct answer: D

Our derived answer: D

So, the stored answer is correct.