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Math Help - cube

  1. #1
    Member Veronica1999's Avatar
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    cube

    Each face of a cube is given a single narrow stripe painted from the center of
    one edge to the center of its opposite edge. The choice of the edge pairing ismade at random and independently for each face. What is the probability thatthere is a continuous stripe encircling the cube?

    I know the total possiblities would be 2 to the 6th power
    but not sure from here....
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  2. #2
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    Re: cube

    Hello, Veronica1999!

    I think I've counted the cases correctly.
    Please check my reasoning.


    Each face of a cube is given a single narrow stripe painted from the center of one edge to the center of its opposite edge.
    The choice of the edge pairing is made at random and independently for each face.
    What is the probability that there is a continuous stripe encircling the cube?

    I know the total possiblities would be 2 to the 6th power, but not sure from here.

    There are 3 orientations for the continuous stripe.

    Code:
              *-------*       *---o---*       *-------*
             /       /|      /   o   /|      /       /|
            /       / o     /   o   / |     o o o o o |
           /       / o|    /   o   /  |    /       /o |
          *-------* o *   *---o---*   *   *-------* o *
          |       |o /    |   o   |  /    |       | o/
          o o o o o /     |   o   | /     |       | o
          |       |/      |   o   |/      |       |/
          *-------*       *---o---*       *-------*
    The other two faces can have their stripes in 2^2 = 4 ways.

    Hence, there are: . 3 \times 4 \,=\,12 ways to have a continuous stripe.

    Therefore: . P(\text{cont. stripe}) \:=\:\frac{12}{64} \:=\:\frac{3}{16}
    Thanks from Veronica1999
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  3. #3
    Member Veronica1999's Avatar
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    Re: cube

    Yay!!! I understand how to do it now.
    Thank you Mr. Soroban.
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