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June 9th, 2013, 08:24 AM   #1
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probability for stick

A stick (letís 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 isnít a good approaching for this problem.
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June 9th, 2013, 09:33 PM   #2
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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
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June 10th, 2013, 02:32 AM   #3
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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?"?
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June 10th, 2013, 01:17 PM   #4
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Re: probability for stick

Quote:
Originally Posted by Hoempa
Isn't this equivalent to asking "what is the probability that the longest segment is larger than half of the length of the stick?"?
Agree, but larger or equal
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June 11th, 2013, 01:08 AM   #5
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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.
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June 15th, 2013, 04:53 AM   #6
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Re: probability for stick

Quote:
Originally Posted by Hoempa
Isn't this equivalent to asking "what is the probability that the longest segment is larger than half of the length of the stick?"?
Something like this but "less than half of the stick"
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June 15th, 2013, 05:25 AM   #7
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Re: probability for stick

Agree; that's what I sais in my last reply: "Agree, but larger or equal".
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