smc

The two parts may round to $0$ and $2$; $1$ and $2$; $1$ and $1$; $2$ and $1$; or $2$ and $0$. By considering the possible ranges for each case, it is easy to see that each case is equally likely (they divide the interval from $0$ to $2.5$, in which one of the parts is found, into five equal ranges of $0$ to $0.5$, $0.5$ to $1$, $1$ to $1.5$, $1.5$ to $2$, and $2$ to $2.5$). As exactly two of the five cases give a sum of $1+2=3$, the answer is $\frac{2}{5}$, which is answer $\boxed{\frac{2}{5}}$.