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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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 Robin Chapman Posts: 412 Registered: 5/29/08
Re: Prob of flipping coin n times, at no time with #h > #t?
Posted: Feb 6, 2013 9:16 AM

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

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