Date: Fri, 28 Jul 95 11:48:42 PDT From: SEONGBIN PARK To: rusin@math.niu.edu (Dave Rusin) Subject: Re: Question: Buffon's "needle problem" Hello, Thank you very much for your reply ! Unfortunately, my math background is very poor and I am not sure what the probability of the problem is. I know the probability should be the possibility of actual outcome divided by all possibilities. But in this case, all possibilities look continuous and the actual outcome seems to be discrete. Could you tell me what the answer is ? I would really appreciate it ! Regards, Seongbin Park (separk@pollux.usc.edu) ============================================================================== Date: Fri, 28 Jul 95 22:43:56 CDT From: rusin (Dave Rusin) To: separk@cs.usc.edu Subject: Re: Question: Buffon's "needle problem" Sorry, I can't recall what the probability comes out to be -- 1/pi or something like that. As you pointed out, when the sample space of possible outcomes is not finite, probability must be computed by some means other than counting (and interpreted suitably, e.g., a probability of zero does _not_ mean something is impossible). In this problem , the set of all outcomes can be tracked with two parameters: the height of the needle's center of mass from the closet horizontal line below that c-o-m, and the rotation of the needle away from the horizontal. All pairs of these parameters (height between 0 and 1, rotation between 0 and 2 pi ) are assumed on physical grounds to be equally likely; one needs only figure out which such pairs imply an intersection and which don't. dave ============================================================================== Date: Fri, 28 Jul 95 23:51:31 PDT From: SEONGBIN PARK To: rusin@math.niu.edu (Dave Rusin) Subject: Re: Question: Buffon's "needle problem" Hello, Thank you very much for your lucid explanation ! Regards, Seongbin Park (separk@pollux.usc.edu)