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

 Messages: [ Previous | Next ]
 Robert Low Posts: 1,458 Registered: 12/6/04
Re: say I flip a coin 100 times...
Posted: Apr 13, 2005 3:55 PM

Ralph Hartley wrote:
> Robert Low wrote:
>> Ralph Hartley wrote:
>>> ken quirici wrote:
>>>> There are 1M people and 100 coins. There are 2**100 possible
>>>> sequences of 100 coins. The chance that 1 out of the 1M will flip
>>>> the same sequence as you is (with ** indicating exponentiation)
>>>>
>>>> 1M * (2**-100) (if I remember correctly you add the
>>>> probabilities of independent events
>>>> to get the probability that they will
>>>> all occcur).

>>>
>>>
>>> You *multiply* the probabilities of independent events to get the
>>> probability that they will all occur. (What you said was wrong, but
>>> what you *did* was correct).

>> Surely not.
> Because 10^6 is much smaller than 2^100 we can ignore the possibility of
> multiple matches.

Oh, OK, I see what you're doing. I hadn't realised you
were making such heavy use of the actual numbers involved.
Fair enough. (Though it does rather require you to
have a good feel for the situation to justify
the approximation. My approach can also be used
by those who, like me, fail to notice such things :-))

Nevertheless, what the OP did was wrong in principle (as
is shown by some of the computations he did) but a good
approximation in the case of interest.

> That gives us 10^6 mutually exclusive events each with
> probability 2^{-100}. Adding the probabilities gives 10^6 * 2^{-100}.
> This is a much better approximation than "2^{-100} is about 8*10^{-31}",
> but it counts trials in which there are 2 matches twice (similarly for
> three matches etc.)

Well, I could give 2^{-100} to more significant figures, but
it didn't seem worthwhile in the context.

And as you point out, I could have used the binomial theorem
to get just as good an answer.

Nice when all the different approaches work out the same
in the end, eh?

--
Rob

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