Date: Sep 19, 2004 9:07 AM
Author: Alexander Bogomolny
Subject: RE: Probability of a Triangle

On Wed, 15 Sep 2004 16:29:58 +0100, Ballew, Pat wrote:
>
>I think I want to try the most direct, what if
>the probability of selecting either
>stick was in the ratio of their length to the whole,
>so if part a was 1/4 "
>and part B was 3/4 " then the prob of picking A is
>1/4 and the prob of >picking B is 3/4... A nice
>extension to the problem.... Any quick solutions?
>


This is pretty simple. For a given h the probability was found to be
h/(1-h). Assuming h < 1/2, this event will occur with probability
(1-h), such that we'll have to integrate [h/(1-h)](1-h) from 0 to 1/2,
with the subsequent multiplication by 1/2. The result is 1/4.

Alexander Bogomolny
http://www.cut-the-knot.org

P.S. I found additional sources for the problem and relevant questions
and am going to expand the article at my site.