Re: flip coins save mankind ...!

Ed Murphy says...
> On Tue, 02 Dec 2003 21:21:17 -0800, Ajit Deshpande wrote:
> 
> > Check this puzzle and answer with reasons behind it.
> > Neo flips a fair coin 20 times. Agent smith spins a fair coin 21
> > times. Agent smith wins if he gets more heads than Neo, else Neo wins.
> > Note that Neo wins if there is a tie. What is the probability that
> > Agent smith wins?
> 
> [spoiler space]
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> Compare Neo's 20 flips to Smith's first 20 spins.  By symmetry, there
> is (a) a X% chance that Neo gets more heads, (b) a X% chance that Smith
> gets more heads, and (c) a (100-2X)% chance that they tie.
> 
> If Smith's 21st spin is a head, then he wins all of (b) and (c), but
> none of (a); the best he can get from (a) is a tie, which Neo wins.
> 
> If Smith's 21st spin is a tail, then he wins all of (c), but none of
> (a) or (b).

Did you mean here that he wins all of (b), but none of (a) or (c)? 

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