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June 9th, 2013, 08:24 AM  #1 
Newbie Joined: Jun 2013 Posts: 8 Thanks: 0  probability for stick
A stick (let’s say a safely match) is broken in four points so five segments are generated, the question is what is the probability that with these segments to be able to construct a pentagon. I solved the problem for two points (triangle) and for three point (quadrilateral) using 2D and 3D representation but I think that for more dimensions it isn’t a good approaching for this problem.

June 9th, 2013, 09:33 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,969 Thanks: 992  Re: probability for stick
Too headachy for me! But for something that would be reasonably close: _._._._._._._._._._ 10 unit stick, with 9 spots (the dots) from which to pick 4 at random. Resulting lengths of the 5 pieces: 1 1 1 1 6 : no 1 1 1 2 5 : no 1 1 1 3 4 : yes 1 1 2 2 4 : yes 1 1 2 3 3 : yes 1 2 2 2 3 : yes 2 2 2 2 2 : yes Probability = 5/7 
June 10th, 2013, 02:32 AM  #3 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: probability for stick
Isn't this equivalent to asking "what is the probability that the longest segment is larger than half of the length of the stick?"?

June 10th, 2013, 01:17 PM  #4  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,969 Thanks: 992  Re: probability for stick Quote:
 
June 11th, 2013, 01:08 AM  #5 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: probability for stick
Hm yes but it wouldn't matter for the outcome I believe. Maybe that's too much of a side question. 
June 15th, 2013, 04:53 AM  #6  
Newbie Joined: Jun 2013 Posts: 8 Thanks: 0  Re: probability for stick Quote:
 
June 15th, 2013, 05:25 AM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,969 Thanks: 992  Re: probability for stick
Agree; that's what I sais in my last reply: "Agree, but larger or equal".


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