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Math Help - probability question

  1. #1
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    probability question

    what's the probability a 1 meter steel broke into 3 pieces that forms a triangle
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  2. #2
    MHF Contributor matheagle's Avatar
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    The 1 meter length is unimportant.
    I assume we're making two cuts uniformly distributed along the bar.
    So let X_1 and X_2 be iid U(0,1) rvs.
    I checked the three case and each case we want the largest cut to be less than .5.
    The cuts are X_1, X_2-X_1 and 1-X_2,
    BUT here I'm assuming X_2>X_1 which is really the order stats.
    I'm trying to figure the logic here.
    We need P(max\{X_1,X_2-X_1,1-X_2\}<.5)
    The joint density of these two is f(x_1,x_2)=2I(0<x_1<x_2<1)
    Last edited by matheagle; May 16th 2009 at 03:01 PM.
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  3. #3
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    is that means Pr(one piece<0.5)=1/2 and the other two we regard them as a whole
    umm.. do u mean it's 1/4?
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  4. #4
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    Quote Originally Posted by camilla_xu View Post
    what's the probability a 1 meter steel broke into 3 pieces that forms a triangle
    It will depend on how the stick is broken.

    Read the attachment and these:

    Stick Broken Into Three Pieces. Solution in Trilinear Coordinates from Interactive Mathematics Miscellany and Puzzles

    Random Triangles

    Problem 8: Random Triangles and an Introduction to Density

    Mathematical Recreations and Essays - Google Book Search
    Attached Files Attached Files
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  5. #5
    MHF Contributor matheagle's Avatar
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    Thanks, I was googling Buffon at 2 :30 am but couldn't find this.
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