smc

The units digits of the powers of $3$ and $7$ both cycle through $1,3,9,7$ in opposite directions, and as $4\mid 100$ each power's units digit is equally probable. There are $16$ ordered pairs of units digits, and three of them $(1,7),(7,1),(9,9)$ have a sum with units digit $8$. Thus the probability is $\frac{3}{16}$ which is $\boxed{\frac{3}{16}}$