The faces of an octahedral die are labeled with digits through . What is the probability, expressed as a common fraction, of rolling a sum of with a pair of such octahedral dice?

On both dice, only the faces with the numbers $3,6$ are divisible by $3$. Let $P(a) = \frac{2}{8} = \frac{1}{4}$ be the probability that Juan rolls a $3$ or a $6$, and $P(b) = \frac{2}{6} = \frac 13$ that Amal does. By the Principle of Inclusion-Exclusion,