Painted Cube

Discrete Mathematics Level 5

The outside of a wooden cube is painted blue. The cube is cut into 27 small cubies, arranged as in a Rubik's Cube. The 27 cubes are placed into a bag. You close your eyes, randomly select a cube and place it on a table.

You then open your eyes and see 5 unpainted faces. What is the probability that the last face (the one against the table) is painted blue?

This problem is not original.
Image Credit: Flickr Marco Braun.

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