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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: 219
Registered: 5/27/08
Prob of flipping coin n times, at no time with #h > #t?
Posted: Feb 6, 2013 8:42 AM
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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)?
Actual problem's a bit more complicated. For m<=n,
what's P_n,m, the prob that #h - #t <= m at all times?
That is, P_n above is P_n,0 here. Equivalently, how
many of those binomial tree paths never get >m past
the "center line"?
John Forkosh ( mailto: where j=john and f=forkosh )

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