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September 11th, 2011, 12:05 PM  #1 
Newbie Joined: Sep 2011 Posts: 1 Thanks: 0  A coin is tossed five times
A coin is tossed five times. By counting the elements in the following events, determine the probability of each event. a. Heads never occurs twice in a row. First I thought it could be: H T H T H or T H T H T but still thinking more this does not seem right. 
September 11th, 2011, 12:41 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: A coin is tossed five times
Remember that tails are allowed to appear more than once in a row.

September 12th, 2011, 07:21 AM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: A coin is tossed five times Hello, nomss! Quote:
I found no formula for this problem. I made an exhaustive list; there are four cases.  
September 12th, 2011, 10:19 AM  #4  
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: A coin is tossed five times Quote:
For five it's easy to take the sum and get 13. Another way of thinking about it: there's one way to do it for length 0 and 2 ways for length 1. For each longer length you can do it in as many ways as the last two added together: the last one followed by tails, or the secondtolast one followed by tails then heads. Thus the answer is the (n+2)th Fibonacci number. Alternately: You're trying to match zero or more tails, followed by a sequence of (heads followed by one or more tails), followed by an optional heads. For those familiar with regular expressions, it can be expressed as Code: T*(HT+)*H? Code: M=[1,1,0;1,0,1;0,0,2]^5;M[1,1]+M[1,2]  

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