To solve this problem, we can start by visualizing the cube and its subdivisions.

The original cube is divided into 8 equal cubes. Each of these smaller cubes can be further divided into 8 equal cubes.

To find the probability that exactly 2 sides of a small cube are painted blue, we need to determine the number of small cubes that satisfy this condition and divide it by the total number of small cubes.

Let's analyze the possibilities:

1. If a small cube is located at the corner of the original cube, then exactly 3 sides of the small cube will be painted blue. There are 8 such small cubes.
2. If a small cube is located on the edge of the original cube (but not at the corner), then exactly 2 sides of the small cube will be painted blue. There are 12 such small cubes.
3. If a small cube is located on a face of the original cube (but not at the corner or edge), then exactly 1 side of the small cube will be painted blue. There are 6 such small cubes.
4. If a small cube is located inside the original cube (not on the corner, edge, or face), then none of its sides will be painted blue. There are 8 such small cubes.

Therefore, the total number of small cubes that have exactly 2 sides painted blue is 12.

Now, let's calculate the total number of small cubes. The original cube is divided into 8 equal cubes, and each of these cubes is further divided into 8 equal cubes. So, the total number of small cubes is 8 x 8 = 64.

Finally, we can calculate the probability by dividing the number of small cubes with exactly 2 sides painted blue by the total number of small cubes:

Probability = Number of small cubes with exactly 2 sides painted blue / Total number of small cubes Probability = 12 / 64 Probability = 3 / 16

Therefore, the correct answer is option A) 3/16.

• Thanks
• Wrong explanation