Just to bug y'all

[hyperbrain]

Pick a chord at random in a circle of radius 1 unit. What do you suppose is the probability that the chord intersects a concentric circle of radius 1/2?

Comments

[hyperbrain]

Damn. But there's one "rigorous" solution, among the solutions.

Re: Bertrand's Paradox

[hyperbrain]

Well, the operative word is "at random". By definition, at random means taking IID (independent and identically distributed) samples. Going by this convention, (1) and (2) result in non-IID samples. (3) is indeed simple and it does give IID samples. The problem actually reduces to the probability that a point picked at random lies in the concentric circle. Simple, eh?

[kandarp]

What's the answer ?

[hyperbrain]

See yodha's answer here and my reply here.