Question

A cube is painted red on all six sides, then cut into 125 smaller congruent cubes. A small cube is selected at random and rolled. What is the probability that it has a red side facing up?

Answer 1

125 = 5³ = 5 · 5 · 5
Every side of a larger cube is cut into 25 congruent squares.
Number of sides of smaller cubes that are painted: 25 · 6 = 150
Number of all sides of 125 cubes: 125 · 6 = 750
Probability : P(A) = 150/750 = 1/5 = 0.2
Answer: probability is 0.2 or 20%