Each face of a cube is painted red or blue, with the colors chosen randomly and independently. The probability that the cube contains at least one vertex such that the three faces of the cube sharing that vertex are all painted the same color is p/q. Find this fraction.

Probability

Each face of a cube is painted red or blue, with the colors chosen randomly and independently. The probability that the cube contains at least one vertex such that the three faces of the cube sharing that vertex are all painted the same color is p/q. Find this fraction.