Random unit cube from a painted 5x5x5 block

The outside of a $5\times5\times5$ cube is painted red, and the cube is then sawn into $125$ unit cubes. You choose one of the small cubes uniformly at random and roll it like a die. What is the probability that the face landing on top is red?

$1/5$. The painted faces total $6\cdot5^2=150$, out of $6\cdot125=750$ small-cube faces in all, and the top face is a uniform choice among them. That gives $\tfrac{150}{750}=\tfrac15$.