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About lottery drawings... - John [entries|archive|friends|userinfo]
John

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About lottery drawings... [Sep. 13th, 2002|01:28 pm]
John
Possibly infrequently asked questions...

Q: So, what were the odds of New York's daily number being 911 on 9/11/2002?
A: 1 in 1000.

Q: But...
A: I know. One in one thousand.

Q:But... but... but...
A: Really, I understand. One in one thousand. That's the long of it, the short of it, and all of it.

Q: BUT! But...
A: Look, on any given day, the chance of *ANY* number coming up is one in one thousand, assuming the numbered ping pong balls that are usually used for drawings are of equal weight, and so forth. Now, I know, you're thinking "but to match the DATE!". The thing is, you'd expect the drawing to match the date on 1/1000ths of the dates on which it's possible to do so.

Q: Still, it has to mean *SOMETHING* that it was on the anniversary of a disaster of that magnitude, in the very place that it happened, doesn't it?
A: Well, see, this is the thing. Nearly random events (like drawings for lottery numbers) don't care about all of the human meanings to days and dates and locations. It's an amazing coincidence, but keep in mind that "coincident" simply means "happening at the same time". (Really, it does. *YOU*, that person with the puzzled look on your face, are thinking of either "mere coincidence" or "chance coincidence", most likely.)

No matter how you play with this, no matter how you measure it, the odds are still the same as they always were. if I go to Vegas, and roll ten sevens in a row at the craps table, the odds I'll get a seven on my next roll is 1 in 6, just like it always is.

Okay... but what if, say, Nostradamus had prophesied "and in the year of the true turning, the great Nye shall face a disaster, losing more than a dozen, dozen, dozen of her people. One year thence, the great Nye's scamsters will truly take it on the chin"? *THAT* would be fascinating. It wouldn't be proof, of course. It wouldn't be a good reason to try to learn anything from the prophecies (would you have guessed anything about "the great Nye" *BEFORE* 9/11/2001?) but it'd make for a fascinating thing to say "Boy... I wonder..." about.

There's a mantra that folks who study probability should chant every time this confounds them. "The law of large numbers doesn't rule out outrageous events; it DEMANDS them".

Let's define a lottery number as "outrageous". What are the odds that an outrageous number will be drawn, a number that has so much personal meaning that it makes people think "Wow... what are the odds?", even though they should know that the answer is "one in one thousand"? Well, if those odds are one in a million, then you'd expect it to happen one time every million drawings. It seems impossible to pull back and say "isn't it fascinating that *THIS* was the particular one-in-a-million rare number that popped up?", but, from a purely intellectual standpoint, that's what you should do.
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Comments:
[User Picture]From: kightp
2002-09-13 01:33 pm (UTC)

Now the truth is revealed ...

... about the inestimable Mr. Palmer's, um, romantic prowess.

Math geekery.

*swoon*

(-;
(Reply) (Thread)
[User Picture]From: eleri
2002-09-13 02:15 pm (UTC)
well, yeah... but we can still go 'oooooh' just cause it's fun to do. Do I place any special significance on it? Well, none other than I believe that random chance can be given an outside nudge by the Imp of the Perverse every once in a while :)
(Reply) (Thread)
[User Picture]From: clauclauclaudia
2002-09-14 11:27 am (UTC)
These are the people that you play out the Monty Hall question with, for cash, until they are enlightened.
(Reply) (Thread)