Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: say I flip a coin 100 times...
Replies: 46   Last Post: Apr 18, 2005 9:42 PM

 Messages: [ Previous | Next ]
 tchow@lsa.umich.edu Posts: 1,133 Registered: 12/6/04
Re: say I flip a coin 100 times...
Posted: Apr 13, 2005 12:17 PM

HERC777 <herc777@hotmail.com> wrote:
>and 1,000,000 other people all flip 100 coins themselves.
>on average, will someone flip the same 100 long sequence I did?
>how long a sequence will they match up to on average?

As clarified later in this thread, what you're asking for is, given a
fixed sequence of coin flips, suppose I generate 1,000,000 other sequences
of coin flips, and take the sequence that best matches my given sequence,
in the sense of having the longest matching prefix. What is the expected
value of the length of this prefix?

For all practical purposes, your "100" can be treated as infinity here, and
I will do so.

The probability that the length of the matching prefix is at most n is
1 - (1/2)^(n+1). With 10^6 series of flips, the probability that the
*longest* matching prefix is at most n is thus (1 - (1/2)^(n+1))^(10^6).
The desired expected value is

sum_(n>=0) n * ( (1-(1/2)^(n+1))^(10^6) - (1-(1/2)^n)^(10^6) )

which works out to be about 20.26.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences

Date Subject Author
4/12/05 HERC777
4/12/05 Jan Burse
4/12/05 HERC777
4/12/05 George Greene
4/13/05 Barb Knox
4/13/05 HERC777
4/13/05 Yajun
4/13/05 HERC777
4/13/05 Jay
4/13/05 HERC777
4/13/05 Jay
4/14/05 Yajun
4/14/05 George Greene
4/14/05 George Greene
4/13/05 Will Twentyman
4/13/05 briggs@encompasserve.org
4/13/05 briggs@encompasserve.org
4/14/05 George Greene
4/14/05 tchow@lsa.umich.edu
4/14/05 briggs@encompasserve.org
4/12/05 Tony
4/13/05 HERC777
4/13/05 ken quirici
4/13/05 Ralph Hartley
4/13/05 Robert Low
4/13/05 Ralph Hartley
4/13/05 Robert Low
4/13/05 tchow@lsa.umich.edu
4/13/05 HERC777
4/13/05 tchow@lsa.umich.edu
4/14/05 HERC777
4/14/05 George Greene
4/14/05 HERC777
4/15/05 tchow@lsa.umich.edu
4/15/05 tchow@lsa.umich.edu
4/16/05 George Greene
4/16/05 HERC777
4/17/05 George Greene
4/17/05 Patricia Shanahan
4/17/05 HERC777
4/18/05 Patricia Shanahan
4/17/05 tchow@lsa.umich.edu
4/18/05 HERC777
4/18/05 George Greene
4/18/05 tchow@lsa.umich.edu
4/18/05 HERC777