Expected painted faces on a random unit cube

The outside of a $10\times10\times10$ cube is painted red, and the cube is then sliced into $1000$ unit cubes. One unit cube is picked at random. What is the expected number of its faces that are red?

$3/5$. By linearity, sum over the six face directions. For each direction exactly $100$ of the $1000$ unit cubes have that face painted, so each face is red with probability $\tfrac1{10}$ and the expectation is $6\cdot\tfrac1{10}=\tfrac35$.