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Topic: Prob of flipping coin n times, at no time with #h > #t?
Replies: 10   Last Post: Feb 14, 2013 2:25 AM

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 JohnF Posts: 218 Registered: 5/27/08
Re: Prob of flipping coin n times, at no time with #h > #t?
Posted: Feb 7, 2013 2:21 AM

Robin Chapman <R.J.Chapman@ex.ac.uk> wrote:
> On 06/02/2013 13:42, JohnF wrote:
>> What's P_n, the prob of flipping a coin n times,
>> and at no time ever having more heads than tails?
>> There are 2^n possible h-t-... sequences of n flips,
>> comprising a binomial tree (or pascal's triangle),
>> with 50-50 prob of going left/right at each node.
>> So, equivalently, how many of those 2^n paths never
>> cross the "center line" (#h = #t okay after even number
>> of flips)?

>
> See the ballot theorem:
> http://en.wikipedia.org/wiki/Ballot_theorem

Thanks, Robin. This sounds very much like the same problem,
but I don't think it actually is.
I'd never heard of the ballot theorem before you mentioned it,
and didn't come across it while intensively trying to google up
a solution before posting. A "semantic web" google should have
suggested it almost immediately, like you did. Just illustrates
that, while search engines are miraculously useful, they still
have an enormous way to go.
--
John Forkosh ( mailto: j@f.com where j=john and f=forkosh )

Date Subject Author
2/6/13 JohnF
2/6/13 Robin Chapman
2/7/13 JohnF
2/14/13 James Waldby
2/14/13 JohnF
2/6/13 RGVickson@shaw.ca
2/6/13 RGVickson@shaw.ca
2/7/13 JohnF
2/7/13 RGVickson@shaw.ca
2/8/13 JohnF
2/8/13 JohnF