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A large wooden cube... (probability)

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A large wooden cube... (probability)

by avenus » Sun May 03, 2009 4:24 am
A large wooden cube, measuring 10 cm on an edge, is composed of smaller cubes, each measuring 1 cm on an edge. The entire outside surface of the assembled large wooden cube is painted red, and the disassembled, with all of the smaller, individual cubes placed in a drum. If one cube is selected randomly out of the drum, what is the probability that the cube selected will have at least one red face?

A. 12:25
B. 61:125
C. 1:2
D. 13:25
E. 3:5
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Re: A large wooden cube... (probability)

by Brent@GMATPrepNow » Sun May 03, 2009 7:37 am
avenus wrote:A large wooden cube, measuring 10 cm on an edge, is composed of smaller cubes, each measuring 1 cm on an edge. The entire outside surface of the assembled large wooden cube is painted red, and the disassembled, with all of the smaller, individual cubes placed in a drum. If one cube is selected randomly out of the drum, what is the probability that the cube selected will have at least one red face?

A. 12:25
B. 61:125
C. 1:2
D. 13:25
E. 3:5
That's a tough one to visualize.
There are 1000 small cubes in total (10x10x10).
Each small cube within the inner 8x8x8 cube will have NO paint.

So, P(selecting a cube with NO paint) = (8^3)/1000
This means that P(selecting a cube with SOME paint) = 1 - (8^3)/1000 = 61/125 (answer choice B)
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by lilu » Sun May 03, 2009 11:10 am
Thank you Brent!
Good question and great explanation! :D
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by criszerriny » Mon May 04, 2009 11:12 am
how was 8x8x8 calculated?

Thanks
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by lilu » Mon May 04, 2009 12:04 pm
criszerriny wrote:how was 8x8x8 calculated?

Thanks
Do you mean WHY 8*8*8 is calculated?
Because if you visualize a cube with a painted surface, you'll have every cube on the top with a painted side and every cube on the bottom with a painted side=10-2=8
Same with the sides: you'll have every cube on each side with one painted side, so 10-2=8 for two opposite sides and 10-2=8 for other two opposite sides.
So, you'll get 8*8*8 cubes that are NOT painted at all.

10^2*6 cubes that have one painted side (100 cubes per surface times 6 sides of the cube)
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by criszerriny » Mon May 04, 2009 1:29 pm
No, I meant How. I understand the reason, just didn't follow the method. Now , I do. Thanks.
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