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06 Sep 2004, 22:46
Kudos
Bookmarks
Hi Folks,
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
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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06 Sep 2004, 23:13
Kudos
Bookmarks
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)
Pb = 480/1000 ~ 1/2
E?
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)
Pb = 480/1000 ~ 1/2
E?
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.
P (red cube ) = 488/1000 = 1/2.
Thanks.
No. of cubes that can be formed from 8 x 8 x 8 = 512.
No. of cubes that are painted red = 1000 - 512 = 488.
P (red cube ) = 488/1000 = 1/2.
Thanks.
Yups. E is right.
