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Four Pins and a Rubber Band (Posted on 2005-02-10) Difficulty: 5 of 5
Four pins are randomly nailed to a square board (according to a uniform probability distribution), and a rubber band is stretched completely around them to form a convex shape. What is the probability that the rubber band is in the shape of a triangle?

See The Solution Submitted by David Shin    
Rating: 4.1000 (10 votes)

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Some Thoughts re: i ve got it | Comment 9 of 11 |
(In reply to i ve got it by Clara Levy)

Four pins are RANDOMALY nailed to a square board.
if this statement is true, then, it could be placed in a triangle, three could be placed in a triangle formation, and the fourth pin could be placed on one of the three sides (between 2)
ie; three dots in a triangle, on one ofthe sides it has three pins(including the corners of course) and the other sides have two dots(just the courners),

SO THEREFORE:
-there isstill a chance of the pins forming a trianle shape, ALTHOUGH i don't know the
exact probability, i think it's around 30%
  Posted by chris on 2005-02-26 06:28:05

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