After taking my Rubik’s cube apart, (leaving me with 12 edge pieces, 8 corner pieces and the center piece) and putting it back together randomly, I noticed that the cube is only solvable sometimes, while other times it cannot be solved by the legal rotations.
Now my question is: What is the probability that a Rubik’s cube that is randomly put together like that is solvable? From trying it out a few times I suspect that the probability is probably lower than $0.5$, maybe something like $[0.2 - 0.3]$, but that’s only a very rough estimate.
I don’t really know how to start on this problem, so any help would be appreciated.