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The six faces of a cube are painted black. The cube is then cut into \(5^3=125\) smaller cubes, all the same size. One of the small cubes is chosen at random, and rolled. What is the probability that when it lands, the face on the top is black?

So I know there are 125-27=98 total cubes with black faces, but how do I find the probability that when it lands the face on top is black? Do I have to find how many cubes have 1 side, 2 sides, 3 sides, etc faces painted black and then find the probability for them? Or is there a faster way?

PS. This problem was never answered to, so this is why I'm reposting it.

:)

May 6, 2020
edited by lokiisnotdead  May 6, 2020

#1
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One, display your latex properly, and two, this is a question from AoPS Intro. to counting and probability.

There's no shame in asking for help, besides, if you go anonomus no one except instructors are going to know you.

also what week is this from?

May 6, 2020
edited by hugomimihu  May 6, 2020
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I think week 6 or 7

LuckyDucky  May 6, 2020
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ummm i think i'm already displaying the latex properly, unless you want me to put all the numbers in latex...

and also, I was just asking for a starting point, not an answer

the main reason i asked for help on this problem here is because it's not aops office hours right now, and i really need to get this problem done

#4
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No, look at the second sentence in your question :D

CentsLord  May 6, 2020
#5
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first one too.

We cant see the numbers

hugomimihu  May 6, 2020
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oh sorry i didn't see that, thanks for pointing it out :)

#6
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I found the one you were looking for, here's the hint

"you can do casework but is there a faster way?"

That's all i'm going to say.

May 6, 2020
#8
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umm ok, thanks ig :)

edited by lokiisnotdead  May 6, 2020
#9
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no rlly that's the hint on the question

I just copied it onto here.

You could do casework but there's a more efficient strategy.

hugomimihu  May 6, 2020
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yeah ik there's a more efficient strategy, but on the 2nd paragraph of my question, you can see that i have no idea what it is

#11
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Welp then you go use case work then sorry!

hugomimihu  May 6, 2020
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oof ok then. thanks for the help :)

#13
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Good luck!

If you need anything else feel free to ask!

hugomimihu  May 6, 2020
#14
+1

There are 125 small cubes.

The total of sides is  750

150 sides are black and the rest of them are bare.

750 : 100%  =  150 : x%

x = 20%

The probability is  20%

May 7, 2020