SOLUTION: A cube has all if its sides painted yellow and then is cut into 729 cubes of the same size. All cubes are placed in an urn are thoroughly mixed, so that the probability of being ra
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Question 1088393: A cube has all if its sides painted yellow and then is cut into 729 cubes of the same size. All cubes are placed in an urn are thoroughly mixed, so that the probability of being randomly picked from the urn is the same for all the cubes. What is the probability that a randomly picked cube has exactly two of its sides painted yellow?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Look at the assembly of cubes made up of 0,1,2, and 3 yellow sided cubes.
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There are 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 or 343 zero sided cubes.
Let's add them all up to make sure we're consistent.
So then the probability of pulling out a two sided cube would be,
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