A cube with edge length 7 units is painted on all faces. It is then cut into 7

^{3} 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**