Mean painted faces on a unit cube from a 10x20x30 block

A solid $10\times20\times30$ block has its outer surface painted red and is then sliced into $6000$ unit cubes. One unit cube is chosen uniformly at random. What is its expected number of red faces?

$11/30$. Every unit of painted surface sits on exactly one small cube, so the total number of red faces equals the surface area $2(200+600+300)=2200$. Dividing by $6000$ cubes gives $\tfrac{11}{30}$.