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Math Help - Triangles - Probability

  1. #1
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    Triangles - Probability

    Consider all of the possibilities of generating a triangle with three diagonals and/or sides of a regular hexagon. In each case, find the probability that a point inside the hexagon is also inside the triangle. Explain each solution.

    to see the picture on this one .. you must click on this link: InterMath

    Can anyone help with this problem?
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  2. #2
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    Re: Triangles - Probability

    Hello, jthomp18!

    The problem involves Counting and some simple geometry.
    Exactly where is your difficulty?


    Consider all of the possibilities of generating a triangle with three diagonals and/or sides of a regular hexagon.
    In each case, find the probability that a point inside the hexagon is also inside the triangle. .Explain each solution.

    To see the picture on this one .. you must click on this link: InterMath

    Case 1: three diagonals.

    There are 2 possible triangles.
    The area of the triangle is \tfrac{1}{2} the area of the hexagon.
    The probability is \tfrac{1}{2}.


    Case 2: two diagonals, one side.

    There are 12 possible triangles.
    The area of the triangle is \tfrac{1}{3} the area of the hexagon.
    The probability is \tfrac{1}{3}.


    Case 3: one diagonal, two sides.

    There are 6 possible triangles.
    The area of the triangle is \tfrac{1}{6} the area of the hexagon.
    The probability is \tfrac{1}{6}.
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