Prime-faced dice with a prime total

Two fair dice each have the six smallest primes, $2,3,5,7,11,13$, on their faces. Both are rolled. What is the probability that the sum of the two faces is itself a prime number?

$\tfrac16$. Two odd primes sum to an even number above 2, and $2+2=4$, so a prime total needs exactly one die showing 2 and the other showing an odd prime $q$ with $q+2$ prime. That works for $q=3,5,11$, each in two orders, giving $6$ of the $36$ outcomes.