homework and exercises - In a ball with random thread/strings, how does the density of threads/strings change with radius?

A large plastic ball full of holes is given. (So the holes are in a plastic shell.) Straight threads connect these holes randomly, by passing through the interior of the ball/shell.

For a big ball or shell, say a meter in size, with thousands of holes, this makes (1/2 times) thousands of straight threads inside it. (Each hole has the diameter of the thread, so that each hole can only have one string passing through it.)

Now the question: Inside the ball/shell (assumed to be large), is the density of the random threads homogeneous, or does it depend on the radius?