Problem #14: Is the Rope Knotted?

A loop of rope is lying on the ground in the position show in the figure below: You are too far away to see which section of the rope is above or below at each of the crossovers at A, B and C.

If we assume that it is equally likely that either section is on top at each crossover, what is the probability that the rope is knotted?

[Top | Solution]