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February 13th, 2010, 05:39 AM  #1 
Newbie Joined: Feb 2010 Posts: 3 Thanks: 0  fair coin tossing, and choosing directions.
I was reading up some introductory discrete probability to use in analyzing randomized algorithms, and I was trying to solve this problem, but couldn't quite nail it. Your city is planned in the form of an infinite grid of crossings. You start from your house, and walk aimlessly. You have a fair coin with you, which you toss to find out which direction to go. You can't turn and walk back, so at each junction you have three choices of direction(front, left, right). Describe a method(give an experiment involving coin tossing) which would let you choose each direction with an equal probability of 1/3. My idea is to toss the coin twice, and decide as follows : if you get 2 heads go left, if a tail and a head, then go straight, if a head and a tail, then go right(the order in which you get head and tail matters). If you get two tails, then toss again. Can someone tell me if this is right?(Is there a better solution?) Or any other ideas about how to approach this problem? Thanks in advance! 
February 13th, 2010, 01:23 PM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: fair coin tossing, and choosing directions. Quote:
 
February 14th, 2010, 05:30 AM  #3 
Newbie Joined: Feb 2010 Posts: 3 Thanks: 0  Re: fair coin tossing, and choosing directions.
Thanks! I'm post a better solution/analysis if I find one.

February 14th, 2010, 05:31 AM  #4 
Newbie Joined: Feb 2010 Posts: 3 Thanks: 0  Re: fair coin tossing, and choosing directions.
Thanks! I'll post a better solution/analysis if I find one. (sorry for the typo in the last post!)

February 14th, 2010, 02:20 PM  #5  
Global Moderator Joined: May 2007 Posts: 6,682 Thanks: 658  Re: fair coin tossing, and choosing directions. Quote:
 

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