Roll a unit
A cube with an edge length of units is painted on all faces. It is then cut into unit cubes. These cubes are put in a bag, one is chosen at random and rolled.
What is the probability the side that faces up is painted?
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1 solution
I'll give the general solution for a nxnxn cube.
When painted 6n^2 unit squares will be painted. There are 6n^3 total sides. The choosing and rolling assure that each of these total sides has the same probability of being chosen.
(6n^2)/(6n^3)=1/n.
So the probability when n=7 is 1/7