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?

Probability that the cord is knottes comes out to be 1/4

Here is how I got to that:
Notation H-high, L-low

Possible combinations are                       
         2                 1                 3              Outcome
         A(H)            A(H)            B(H)          no Knot
         A(H)            A(H)            B(L)          no Knot 
         A(H)            A(L)            B(H)          Knot  
         A(H)            A(L)            B(L)           no Knot 
         A(L)            A(H)            B(H)          no Knot
         A(L)            A(H)            B(L)           Knot 
         A(L)            A(L)            B(H)           no Knot  
         A(L)            A(L)            B(L)           no Knot

Well for the ongoing discussion on whats to be considered as a knot, my take is, The cord should be considered knotted if on pulling the cord from A and B, a knot is formed. 

Posted by Rupesh Khandelwal on 2005-08-05 10:32:14