A cube, all of whose faces are painted, is sawn into 125 identical cubes.

A cube, all of whose faces are painted, is sawn into 125 identical cubes. All cubes are shuffled. Determine the probability that a dice drawn for luck will have three colored faces.

To determine the probability, we use the following classical formula: P (A) = n (A) / n,

where n (A) is the number of outcomes favorable to event A, n is the total number of equally possible outcomes.

Let’s determine the number of outcomes favorable to the event:

There will be 4 such cubes in the upper corners of the cube and 4 in the lower corners. Therefore, there are only 8 cubes.

Let us determine the probability that a dice drawn for luck will have three colored faces:

8/125 = 0.064.

Answer: The probability of an event is 0.064.