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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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Posts: 181
Registered: 5/27/08
Re: Prob of flipping coin n times, at no time with #h > #t?
Posted: Feb 7, 2013 2:21 AM
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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 )

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