# Math Help - Common Fraction

1. ## Common Fraction

A large cube is dipped into red paint and then divided into 125 smaller congruent cubes. One of the smaller cubes is then randomly selected. What is the probability that the cube selected will have at least 25 percent of its surface area painted red? Express your answer as a common fraction.

2. Originally Posted by aznmartinjai
A large cube is dipped into red paint and then divided into 125 smaller congruent cubes. One of the smaller cubes is then randomly selected. What is the probability that the cube selected will have at least 25 percent of its surface area painted red? Express your answer as a common fraction.
Hello,

the surface of a cube exists of 6 squares. At least 25% of the surface must be painted that means that there are at least 2 squares of the surface painted in red.

You find 12 * 3 cubes with 2 painted squares along the edges (12) of the origianl cube
and 8 cubes with 3 painted squares at the vertices of the original cube.

Total 44 of 125 cubes have at least 25 % of their surface painted. Thus the probability is:

$p=\frac{44}{125}=\frac{11}{25}$

EB

3. Thanks so much Earboth =)