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Politics : Formerly About Advanced Micro Devices
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To: andreas_wonisch who wrote (128122)11/10/2000 6:43:25 PM
From: Ali Chen  Read Replies (1) of 1583744
 
Andreas, OT<The expectation is evidently n*p = 2000 * 0.5 = 1000 and the probability for getting at least 1000 heads is 0.5. That's also what intuition is telling us...>

Your formula n*p and is absolutely correct, but
the formal conclusion about 0.5 is not. This is
exactly the basic definition of 0.5 probability:
when flipping a coin 2000 times, expect any side
to appear about 1000 times, almost certainly.

<Or do you expect to get with almost certainty (98.5%) at least 10 heads when flipping a coin 20 times?>

With 20 attempts I expect to have 10 heads with
probability of 1-0.5/sqrt(20), or 94%. As the
number of attempts grows, the confidence interval
shrinks as square root from the total number of
attempts, possibly with some numerical factor
of the order of 1 I don't remember exactly.
With infinite amount of attempts you will get
1000 heads for sure.

Disclaimer: the terms and definitions used above
may be slightly different from one science field
to another.

Regards,
- Ali

P.S. I just saw your precise Math. The width of
your distribution function narrows as sqrt(N) too.
We are talking in different terms here. To get _exactly_
1000 out of an _event_ with 2000 attempts, you may be
right. But if we think about getting 999, 1000, or 1001
in a single 2000-fold attempt, the probability is 0.98.
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