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Math Help - Triangle Formation Probability

  1. #1
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    Triangle Formation Probability

    A stick is cut into 3 in a uniformly random manner. What is the probability that all three will form a triangle?
    Probability Puzzles: Cutting a Stick to form a Triangle
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    MHF Contributor ebaines's Avatar
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    Re: Triangle Formation Probability

    The pieces can't make a triangle if any one of the three piece is greater than half the length of the stick. Imagine a stick 1 meter in length, and the locations of the two cuts are measured from the left end of the stick. Call the two points of the cuts A and B. The pieces will not be able to form a triangle if (A> 0.5 and B> 0.5) or (A< 0.5 and B<0.5) or (A<0.5 and B> A+0.5) or (A > 0.5 and B< A-0.5). You can add these up to get the probability that the pieces won't make a triangle is 0.75. Hence the probability that they do make a triangle is 0.25.
    Last edited by ebaines; December 18th 2012 at 10:15 AM.
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    Re: Triangle Formation Probability

    Yes, thanks for the input. That is also a nice different way to look at the puzzle.
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