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A point in space $(x,y,z)$ is randomly selected so that $-1\le x \le 1$,$-1\le y \le 1$,$-1\le z \le 1$. What is the probability that $x^2+y^2+z^2\le 1$?

 Mar 12, 2021
 #1
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Not sure if this is correct.

 

Ok there are three possibilities for x, y, and z --------> -1, 0, and 1

 

For \(x^2 + y^2 +z^2 \leq 1\), at least two of the numbers have to be 0.

 

I don't know how to continue. Help.

 Mar 12, 2021
 #2
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But can't the $x, y,$ or $z$ be a decimal?

Guest Mar 12, 2021
 #3
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Help ASAP pls smiley

 

Thanks in advance

 Mar 12, 2021
 #4
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By geometric probability, the answer is pi/8.

 Mar 21, 2021

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