Bagged Rubik's cubelet showing five blank faces

A Rubik's cube whose outside is coloured is taken apart into its 27 small cubes, which go into a bag. You pick one at random and toss it; when it lands, the five faces you can see are all uncoloured. What is the probability you picked a small cube that has exactly one coloured face?

$1/2$. Only the hidden centre cube (no colour) or one of the 6 face-centre cubes landing coloured-side down can show five blank faces. These have weights $\tfrac1{27}$ and $\tfrac6{27}\cdot\tfrac16=\tfrac1{27}$, so they are equally likely.