My Math Forum root with probability

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 March 2nd, 2018, 09:16 AM #11 Senior Member   Joined: Nov 2011 Posts: 184 Thanks: 2 Thanks!!! I think that the question will be solve by computer. Right?!
March 2nd, 2018, 10:06 AM   #12
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Quote:
 Originally Posted by AngleWyrm2 Given a set of points on a cartesian coordinate system of x,y, the distance from origin to any point is sqrt(x^2 + y^2). What radius of distance from origin will include 50% of randomly distributed new points, where x and y range from 0..k?
This is barely a problem in probability.

It would be a better problem if $x,y \in \mathbb{R}$ as this would allow an exact answer.

Since you imply a uniform distribution of points we simply have to find the radius such that the areas of the two regions are equal.

i.e.

$k^2 - \pi r^2 = \pi r^2$

$k^2 = 2 \pi r^2$

$r = \sqrt{\dfrac{k^2}{2\pi}} = \dfrac{k}{\sqrt{2\pi}}$

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