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JohnF
Posts:
151
Registered:
5/27/08


Prob of flipping coin n times, at no time with #h > #t?
Posted:
Feb 6, 2013 8:42 AM


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 ht... sequences of n flips, comprising a binomial tree (or pascal's triangle), with 5050 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: j@f.com where j=john and f=forkosh )



