A cube with edge 4, all faces of which are painted, was sawn into 64 unit cubes, the resulting cubes

A cube with edge 4, all faces of which are painted, was sawn into 64 unit cubes, the resulting cubes were mixed and put into a bag. Find the probability that a dice taken at random will have at least two painted faces

Recall from the outset that probability is the ratio of the number of favorable events to the total number of possible events that form a complete group.

In our problem, 4 options are possible: 3 colored faces, 2, 1 and no colored faces. In the latter case, we are talking about 8 inner cubes.

Further, on each face of the cube there are 4 cubes with one colored face. Then there are 4 * 6 = 24.

Therefore, the desired probability will be equal to:

P = (64 – 8 – 24) / 64 = 32/64 = 0.5.

Answer: P = 0.5.