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Math Help - Tough Probability Example

  1. #1
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    Tough Probability Example

    This question is hard to picture on paper. Could someone please help me visualize what is going on in this problem? Thanks in advance!! (The photo hase some issues and the textbook does not give a visual aid for this example.

    In a forest there are n trees per hectacre evenly spaced. The thickness of each trunk is D. What is the distance of the wood not seen for the trees? (Find the probability that the line of sight will hit a trunk within a distance x.)

    This is the part I cannot picture visually.

    Imagine a circle with radius x around the observer. A portion, s(x), where 0 < s(x) < 1, is covered by trees. The observer moves a distance dx outward, and another circle is drawn.
    (Starting here I don't understand) There are 2(pi)n x dx trees growing in the annulus limited by these two circles. They hide a distance 2(pi)x n D dx or a fraction n D dx of the perimeter of the circle.


    Again, thanks in advance for the visual aid!!
    Attachment 28983
    Last edited by zachd77; August 14th 2013 at 05:15 AM.
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  2. #2
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    Re: Tough Probability Example

    Quote Originally Posted by zachd77 View Post
    This question is hard to picture on paper. Could someone please help me visualize what is going on in this problem? Thanks in advance!! (The photo hase some issues and the textbook does not give a visual aid for this example.

    In a forest there are n trees per hectacre evenly spaced. The thickness of each trunk is D. What is the distance of the wood not seen for the trees? (Find the probability that the line of sight will hit a trunk within a distance x.)

    This is the part I cannot picture visually.
    [B]
    The problem is not well defined (e.g what is trunk's thickness?) but assuming:
    a)The forest has infinite area.
    b)The trunk has a shape of a circle(cylinder actually what you know what i mean) with diameter D.

    Then you just have to find the probability the inside blue circle of the below image(for some x and then for all x's**) to cross at least one of the 4 circles that are in its corners:
    **The circle is produced by having a center of the blue circle, that moves in all the square area and in its perimeter and has a radius x.
    Last edited by ChessTal; August 14th 2013 at 05:50 AM.
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  3. #3
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    Re: Tough Probability Example

    This problem has nothing to do with probability!
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  4. #4
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    Re: Tough Probability Example

    I know, it's a strange question. But I'm still confused onto how you can determine the number of trees in the annulus.
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