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

August 22, 2021 | education

| **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.

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