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A large cube 10cm on a side is composed of smaller cubes 1 cm on a side. The large cube is printed red on its outside surfaces and then all the cubes are mixed in a drum. If one cube is selected randomly, which of the following is the approximate probability that the cube will have at least one red face?
A) 1:6
B) 1:5
C) 1:4
D) 1:3
E) 1:2
My flawed solution - 1000 small cubes contained in the big cube. Each side has 10*10 = 100 cubes. So 6 outer sides of the large cube have 600 small cubes. Since large cube is painted on outside surfaces - these 600 small cubes are painted red - while 1000-600 = 400 cubes are not painted.
P(atleast one side painted) = 1- P(no side painted) = 1 - 400/1000 = 3/5
Evidently not one of the ans choices - what am I missing?
Thanks
Stuti
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Total numbe rof small cubes = 1000
Total number of cubes with atleast 1 red side = 6 x 100 - 12 x 10 = 480
(6 sides have 100 small ubes each; Each of the 10 cubes in the 12 edges has been accounted for in two sides' count. So we have to subtact 120)
totally there are 1000 small cubes. Only the outer layer of the larger cube is painted red. Therefore the cube which is one layer inside the outer layer ( 8 x 8 x 8) is not painted red.
No. of cubes that can be formed from 8 x 8 x 8 = 512.
No. of cubes that are painted red = 1000 - 512 = 488.
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