Civil Liberties

[lweiger at umich.edu]

Is that a reference my inscrutable habit of jumping from thread to thread? 
If so, it's a good one.  I don't know if I can explain it any more clearly 
than I have, but I'll try again: you are no more likely to win in any 
individual (if I knew HTML, I would've italicized that) drawing by 
participating more often.  Collectively, though, you are more likely to 
eventually win.  However, if you're unlucky enough to go through 999,999 
lotterys without a win, the millionth time is no more likely to be a charm. 
Even better than playing a million times would be purchasing every 
combination (discounting the fact that doing so generally results in a net 
loss of money on the purchaser's part).

(If you really want to have fun with probability, discuss the "three doors" 
problem sometime, which has made more than a few statistics profs look like 
asses.)

-- Luke

--On Wednesday, September 19, 2001 11:00 PM -0400 Max Sawicky 
<sawicky at bellatlantic.net> wrote:


> No, grasshopper.  Since the odds are the
> same each time, you are no more likely
> to win if you play a million times than
> if you play once.  If you play a million
> times, the likelihood of someone other
> than yourself winning is also multiplied
> a million times.  One in a million and
> ten in ten million are the same odds.
>
> mbs
>
>
> No, Carrol's right.  Although I'm not a number cruncher, it's quite clear
> that the probability of getting the non-white ball (or rolling a five) is
> far greater if you perform the experiment many times.  Think of it this
> way: someone who plays the lottery often for the entirety of their life
> is  more likely to win at some point (even though their odds don't
> increase  with each succesive failure) than another person who buys a
> single ticket.
>
> -- Luke
>
> --On Wednesday, September 19, 2001 8:49 PM -0400 Max Sawicky
> <sawicky at bellatlantic.net> wrote:
>
> > I don't think so.  YOu're thinking of an experiment
> > that would go like this -- a very large urn has a
> > million balls in it, all but one white.  If you
> > draw all the balls, obviously one of them will
> > be white.  But if you draw and replace, then in
> > each draw your chances of coming up white are
> > still one in a million.  So your premise depends
> > on the trials being dependent on each other. Each
> > null result increases the likelihood of a non-null
> > result subsequently.  So it depends on exactly what
> > we're talking about, which I have forgotten.
> >
> > mbs
> >
> >
> > Yes. This is tricky, but probability, as I understand it, is not really
> > a matter of prediction. So what we are talking about is a situation not
> > before the millionth & one roll of the dice but _after_ all 1 million
> > and one rolls have occurred, and we know the results of NONE of the
> > rolls. What is the probability that when we open the record books to
> > check on what has happened that someplace in that record a roll of five
> > has occurred.
> >
> > Carrol
>
>
>