A white 4x4x4 cube is painted red, then sliced into 1x1x1 cubes, some of which have no red sides, some have one red side, ...
All of the 1x1x1 cubes are put in a bag. You draw one at random (you can't feel any difference between painted and unpainted sides) and then toss this cube. What is the probability that a red side will be on top?
There is a laborious way to solve this and a way you can do in your head. Luckily, they give the same answer! ;-)