Problema Solution
A larger cube is created from 64 white unit cubes. Two opposite faces of that larger cube are painted black, and the remaining four faces are painted red. The unit cubes then are placed in a bag. If one unit cube is drawn at random, what is the probability that it has two red faces and one black face? Express your answer as a common fraction.
Answer provided by our tutors
8*8 = 64
8*2 = 16 black faces
8*4 = 32 red faces
64*4 = 256 total faces
256 - 32 - 16 = 208 white faces
we want two red faces and one black face, so that is one of the corner cubes on each of the black-faced sides
4*2 = 8 cubes with two red faces and one black face
8/256 = 0.03125
there is approximately a 3.1% probability of drawing out a cube with two red faces and one black face