Question

A 3x4x5 rectangular cuboid (e.g. a brick) is painted blue and cut into 1x1 cubes. what is the expected value for the painted sides of a randomly selected cube?

Answer 1

8 cubes are painted on 3 sides

24 cubes are painted on 2 sides

22 cubes are painted on 1 sides

6 cubes are painted on 0 side

E = 3 * 8/60 + 2 * 24/60 + 1 * 22/60 + 0 * 6/60 = 47/30 = 1.567