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if n=2 P=1
if n>3 P<1
....

\[P(n)\]

ill post my thoughts so far.

trivially P(1) = 1

this question reminds me of Buffon's needle problem

now for three points

is P(3)=1/2?

yes i think so! maybe..
|dw:1333724818545:dw|

placing C on the circle somewhere.. where is allowed?

maybe its not 1/2 ...

1/2 in the worst case scenario, ie if the first two points are opposite

|dw:1333725166177:dw|
i think its \[\frac{l}{(circumference)}\]

those lines from A and B are diameters

thanks for the help

50 percent

I agree, good question
This is perhaps a good question for the meta-math section

whats the meta math section?

click the "mathematics" blue bar
you will see it is a category

hard and irregular questions are found and solved there

oh cool

or both? hehe

I'm not sure if you can post in both sections with the new "bump" system, but feel free to try :)

oh, mr.math is here after all
maybe he has some nice thoughts on this

I found this http://mathproblems.info/images/prob1.pdf

I liked this answer: http://math.stackexchange.com/a/18371/2109

I can see how they're kinda the same...

gonna close it up now unless anyone has more to add, thanks guys for all your help :)