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?
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