All six faces of a cube are painted blue. The cube is then cut into 125 smaller cubes, all the same size. One of the small cubes is chosen at random, and rolled. What is the probability that when it lands, the face on the top is blue?
See a slight variation to the question here: https://www.quora.com/A-cube-is-painted-blue-on-all-faces-and-divided-into-125-smaller-cubes-of-equal-size-How-many-cubes-are-not-painted-on-any-face
There are 125 smaller cubes, each with 6 sides, so there are 750 total faces. Each face of the original cube has a 5x5 square of blue faces, so there are 25 blue faces for each side of the original cube, for a total of 150 blue faces. 150/750=1/5
