I was walking along the road one day when I spied a cord of some sort lying in my path. From my vantage point, as I was approaching the cord, I could not tell if it was knotted or not.
What is the probability that the cord was knotted?
The problem lies in determining which of the lines are lying on top of each other at each intersection (1, 2, 3). Tracing the cord from end A to end B, the line we're following can be either Over or Under the line that's being intersected. The table below lists the eight possible scenerios and whether or not the cord is knotted:
| 1 2 3 | Knot / Not
---+-----------+------------
1 | O O O | N
2 | O O U | N
3 | O U O | K
4 | O U U | N
5 | U O O | N
6 | U O U | K
7 | U U O | N
8 | U U U | N
As can be seen, there are eight possible ways the cord could be lying and in only two of the eight is the cord knotted. Therefore, the probability that the cord is a knot is 2/8 or 25%.
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