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# A large cube 10 cm on a side is composed of cubes 1 cm on a

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CEO
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A large cube 10 cm on a side is composed of cubes 1 cm on a [#permalink]

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15 Jul 2006, 00:19
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A large cube 10 cm on a side is composed of cubes 1 cm on a side. The outside of the large cube is painted red and then all of the individual cubes are mixed in a drum. If two cube is selected randomly what is the probability that first cube has exactly one red face and second has exactly two red faces?
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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15 Jul 2006, 01:58
We have 10x10x10 large cube that consisits of 1000 1x1x1 small cubes.
we have 488 painted cubes. 8 have 3 red sides, 6*64=384 have one red side and 12x8=96 have 2 red sides.
Required prob is (384/1000)*(96/1000)
CEO
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15 Jul 2006, 02:06
BG wrote:
We have 10x10x10 large cube that consisits of 1000 1x1x1 small cubes.
we have 488 painted cubes. 8 have 3 red sides, 6*64=384 have one red side and 12x8=96 have 2 red sides.
Required prob is (384/1000)*(96/1000)

You did everything right except bold part

(384/1000)*(96/999)
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15 Jul 2006, 02:18
Thanks Dahia, forgot the conditional stuff part
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Re: PS: Another Cube Probability. [#permalink]

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22 Jul 2006, 20:19
ps_dahiya wrote:
A large cube 10 cm on a side is composed of cubes 1 cm on a side. The outside of the large cube is painted red and then all of the individual cubes are mixed in a drum. If two cube is selected randomly what is the probability that first cube has exactly one red face and second has exactly two red faces?

The cube has 6 surfaces. On each surface there are exactly 8x8 or 64 cubes painted on 1 surface. Total number of cubes painted on 1 surface is therefore 64x6=384

The cube has 12 surface edges. On each surface edge, there are 8 cubes that are painted red on 2 surfaces. Total = 8x12=96

Therefore the prob = 384/1000 x 96/999
Re: PS: Another Cube Probability.   [#permalink] 22 Jul 2006, 20:19
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