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 ]
 George Greene Posts: 448 Registered: 12/12/04
Re: say I flip a coin 100 times...
Posted: Apr 12, 2005 10:05 PM

HERC777 wrote:
> there's about 1,000,000 combinations of a sequence of 20 coin flips
> 2^10 = 1024
> 2^20 = a million
>
> so on average they should copy your sequence up to the 1st 20 flips..
>
> Agree?

No. Jesus.
First of all, you have to know what you are
averaging OVER. You are overaging over FLIPPERS,
or flip-sequences. You are averaging over a million
things. For each of these million strings (of H or T),
you want to know how long its prefix-matching-you is.
The number of flippers matching-you-so-far starts out
at a million after 0 flip-positions and falls by half
with every flip(in time) thereafter. Half the million
will flip opposite from you on the first flip and so
will have a prefix-matching-you of length 0.
1/4 of them will match you on the first flip and
miss on the 2nd, and have a match-you length of 1.
1/8 of them will match you on the first two but miss
on the 3rd, and have a match-you length of 2.
On the 20th flip, the EXPECTED number of flippers
continuing to match you all this way will be less than 1.
Furthermore, the AVERAGE, over all flippers, of the
initial-length-of-match-you-prefix, is ALSO
LESS THAN 1.

NOT 20.

This is HIGH SCHOOL algebra, herc.

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