[net.math] More Heads than Tails

colonel@gloria.UUCP (Col. G. L. Sicherman) (06/13/85)

[% dead cockatrice]

> 	Suppose you have a counter, initialized to 0.
> Flip a fair coin N times, incrementing the counter whenever the coin
> comes up heads, and decrementing the counter whenever the coin comes up tails.
> What is the probability that the counter never dipped below 0.
> N	1	2	3	4	5	6	7	8
> odds	1/2	2/4	3/8	6/16	10/32	20/64	35/128	70/256

By inspecting the table, it's C(n, n div 2)/2^n.  There's
probably a simple proof.
-- 
Col. G. L. Sicherman
...{rocksvax|decvax}!sunybcs!colonel