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> The outer surface of a 3x3 Rubik's cube is painted red. You break the Rubik's cube into 27 smaller cubes. You select 1 at random and put it on the table. You see that the 5 visible spaces have no red painting. What is the probability that the bottom face is painted red?
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So I am given that the selected cube has 5 faces that are not painted red. This eliminates 20 of the cubes. The remaining cubes are the 6 centered cubes on each of the 6 faces, and the very center cube.

So isn't the probability simply 6/7? There is a hint that says to use Bayes theorem, but I don't see how that comes in. All that is needed seems to be just the definition of conditional probability. Specifically we want $P(A\mid B)$ where $A$ is the event that the selected cube has 1 painted face and $B$ is the event that the selected cube has 5 un-painted faces.