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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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soln Comment 2 of 2 |
prob. is the number of each type (corner, edge, face, interior) = 
(8, 60, 150, 125) weighting the likelihood of a painted face up:
(3/6, 2/6, 1/6. 0/6) over the number of cubes: 7^3

sum[ number x likelihood ]  / sum [cubeletts ] = 49 / 7^3 =1/7

posted later: Charlie's way was way slicker! (I wasted a piece of paper.)

Edited on November 6, 2019, 10:37 am
  Posted by Steven Lord on 2019-11-06 10:32:01

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