### Home > CCA2 > Chapter 2 > Lesson 2.1.3 > Problem2-41

2-41.

Suppose you have a 3 by 3 by 3 cube. It is painted on all six faces and then cut apart into 27 pieces, each a 1 by 1 by 1 cube. If one of the cubes is chosen at random, what is the probability that: Homework Help ✎

1. Three sides are painted?

This cube will have 3 faces painted. How many cubes like this are there in the figure? How many cubes are there altogether?

$P(3\text{ sides painted})=\frac{8}{27}$

2. Two sides are painted?

$P(2\text{ sides painted})=\frac{12}{27}$

3. One side is painted?

How many cubes have one face exposed?

4. No sides are painted?

How many cubes have 1, 2, or 3 faces painted? How many are left?