The problem statement: And here is the textbook solution: Note that the the simple calculation makes use of the Boole's inequality and the reasoning itself is the Probabilistic method And my questions are: Where do they use that those are cubes? What breaks down if we just go through the same line of reasoning with any 8 point figure? Say, with a parallelepiped which is not as demanding as a cube? How do we know that the 0.2 is about cubes? Any help is highly appreciated.