smc

There are $3$ cases where the running total will equal $3$: one roll; two rolls; or three rolls: Case 1: The chance of rolling a running total of $3$, namely $(3)$ in exactly one roll is $\frac{1}{6}$. Case 2: The chance of rolling a running total of $3$ in exactly two rolls, namely $(1,2)$ and $(2,1)$ is $\frac{1}{6}\cdot \frac{1}{6}\cdot 2=\frac{1}{18}$. Case 3: The chance of rolling a running total of 3 in exactly three rolls, namely $(1,1,1)$ is $\frac{1}{6}\cdot \frac{1}{6}\cdot \frac{1}{6}=\frac{1}{216}$. Using the rule of sum we have $\frac{1}{6}+\frac{1}{18}+\frac{1}{216}=\boxed{\frac{49}{216}}$.