The six faces of a cube are painted black. The cube is then cut into \(5^3=125\) 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 black?
So I know there are 125-27=98 total cubes with black faces, but how do I find the probability that when it lands the face on top is black? Do I have to find how many cubes have 1 side, 2 sides, 3 sides, etc faces painted black and then find the probability for them? Or is there a faster way?
Thanks and please help!