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Roll a unit (Posted on 2019-11-06) Difficulty: 3 of 5
A cube with edge length 7 units is painted on all faces. It is then cut into 73 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?

See The Solution Submitted by Jer    
Rating: 1.0000 (2 votes)

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Solution In-the-head solution (spoiler) | Comment 1 of 2
There are 7^3 cubes, each with 6 sides, so there are 7*7*7*6 faces that each have the same probability of being the upturned face.

There are among them 7*7*6 faces that are painted.

The probability is 7*7*6 / (7*7*7*6) = 1/7 that the upturned face is painted, though I really dislike having to put those parentheses in.  Most formulae would be easier to read (fewer parentheses needed) if the convention of multiplication taking precedence over division were not just the province of the physicists.

  Posted by Charlie on 2019-11-06 10:31:12
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