A cube is painted red on all six sides, then cut into 125 smaller congruent cubes. A small cube is selected at random and rolled. What is the probability that it has a red side facing up?

Question

A cube is painted red on all six sides, then cut into 125 smaller congruent cubes.   A small cube is selected at random and rolled. What is the probability that it has a red side facing up?

anonymous · Answer

I got 0.176

anonymous · Answer

I got ------ 8 pieces of cube with 3 sides painted red
                     36 pieces of cube with two sides painted red
                     and 36 pieces of cube with one side painted red

dumbcow · Answer

not quite, there are 54 cubes with 1 red side
corners have 3 red sides
edges have 2 red sides
outer faces have 1 red side
inner cube have 0 red sides
|dw:1344693971960:dw|
to get probability, multiply individual probabilities for each case, then take sum
probability of getting a corner is 8/125.....chance of landing on red is 3/6
--> (8/125)*(3/6) = 4/125
probability of getting an edge is 36/125.....chance of landing on red is 2/6
--> (36/125)*(2/6) = 12/125
probability of getting outer face is 54/125.....chance of landing on red is 1/6
--> (54/125)*(1/6) = 9/125
of course the probability for inner cubes is zero since they have 0 red sides

--> 4/125 + 12/125 + 9/125  = 25/125 = 1/5