AMC 12 Mock Exam 3 Problem 13

There are $48$ equally likely outcomes, and the possible prime sums are $2,3,5,7,11,13$. For a sum $s$, count the values $a\in\{1,\dots,6\}$ with $1\le s-a\le8$: $s=2$: $1$; $s=3$: $2$; $s=5$: $4$; $s=7$: $6$; $s=11$: $a=3,4,5,6$, i.e., $4$; $s=13$: $a=5,6$, i.e., $2$. That is $19$ outcomes, so the probability is $\boxed{\tfrac{19}{48}}$.