1. ## 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....

2. ## Re: cube

Hello, Veronica1999!

I think I've counted the cases correctly.

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: . $P(\text{cont. stripe}) \:=\:\frac{12}{64} \:=\:\frac{3}{16}$

3. ## Re: cube

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