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JohnF
Posts:
97
Registered:
5/27/08
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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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