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I believe you may be mistaking a Gaussian distribution for a probability.
Probability theory does not say that every flip of 100 coins will yield 50
heads and 50 tails, only that there will be a Gaussian distribution of yields
(in the real world), in which the ratio of, say, heads to the total number of
flips, will ultimately approach 0.5 as one increases the total number of
flips. It is entirely possible to get 100 heads out of 100 flips, it's just
very improbable (specifically, 1/(2^100)), and even if the first 100 flips
produced all heads, if you kept flipping, the ratio of heads to the total
number of flips, as time goes, by, will get closer and closer to 1/2, even
though the first 100 flips were all heads. Another way of saying this is that
even for only one flip, the probability of it coming up heads is still 1/2.
The fact that the first flip comes up either heads (1.0) or tails (0.0) does
not negate the fact that the probabililty of it coming up heads was 0.5 ---
you've only flipped it once, and what you obtain in the real world more and
more closely matches what you'd expect from probability theory as you increase
the number of observations (flips).
Fred wrote:
> On Sun, 2 Dec 2001 14:04:22 -0800, you wrote:
>
> >Now in my mind, these two different probabilities are measuring the *same
> >event*.
>
> Not exactly. The probabilities apply over very large numbers of
> events, but NOT over very few events.
>
> Think about this:
>
> If you toss a penny 100 times the probability is that 50 will be heads
> and 50 will be tails.
>
> Would you take a bet that after 100 tosses the results will be
> EXACTCLY 50 heads?
>
> Don't do it.
>
> As you get towards 100 tosses you are LESS likely to have exactly 50
> heads, but more likely that the overall percentage will be CLOSER to
> 50% heads. IF you tossed 1,000 times the percentage will be even
> closer to 50/50 but even less likely to be EXACTLY 500 heads and 500
> tails after toss number 1,000.
>
> "Success is the only test of genius" -R.Adm Daniel Gallery 1901-1977
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