Question 1088393
Look at the assembly of cubes made up of 0,1,2, and 3 yellow sided cubes.
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*[illustration CUBE.JPG].
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There are {{{9^3}}} cubes in all.
There are 8 three sides cubes, one for each corner.
Along every edge, there are 7 two sided cubes. 
There are 12 edges making a total of 84 two sided cubes.
Each face has 49 one side cubes, there are 6 faces for a total of 294 one sided cubes.
The inner cubes have zero painted sides. 
There are {{{7^3}}} or 343 zero sided cubes. 
Let's add them all up to make sure we're consistent.
{{{729=343+294+84+8}}} 
{{{729=729}}}
So then the probability of pulling out a two sided cube would be,
{{{P=84/729}}}
{{{P=28/243}}}