d The only cube(s) that are not painted are within the big cube.
A
a 8/27
B
b 4/9
C
c 2/9
D
d 1/27
Practice makes perfect
a Probability is calculated by dividing the number of favorable outcomes with the number of possible outcomes.
P=Number of favorable outcomes/Number of possible outcomes
Any piece that is painted on three sides must be placed on one of the cube's corners.
The cube has 4 pieces on the top layer and 4 on the bottom layer for a total of 8 pieces painted on all three sides. Since the whole cube consists of 3^3=27 cubes, we can determine the probability of picking a side with three painted sides.
P(three sides are painted)=8/27
b Any piece of the cube that sits on the edge but not in a corner is painted on two sides.
There is one piece on each edge of the cube. Since the cube has 12 edges, there are 12 pieces that are painted on two sides. Now we can calculate the probability of picking a side where two sides are painted.
P(two sides are painted)=12/27=4/9
c For a piece to be painted on only one side it must sit in the center of one of the cube's faces.
The cube has 6 faces, so there are 6 of these pieces. With this information, we can calculate the probability of only one side being painted.
P(one side is painted)=6/27=2/9
d There is only one unpainted side in the cube, namely the one in the middle.
With this information, we can calculate the probability of picking the one unpainted cube.
P(no side is painted)=1/27
