Significance is an illusion.
If you draw two three-digit numbers the odds of coming up with 911 at least once are (about) 1 in 500, as has been pointed out here. The odds of this happening on a particular date such as 9/11 are no greater or no less, as has also been pointed out. However, if you think not of that particular day, but of the date of ANY day being drawn, then you must remove from 365 all the dates which cannot occur in a three-digit combination.
(Note: I am not including leading zeroes in single digit months, since for consistency we'd then have to use leading digits in the day as well, and there could be no such three-digit dates.)
The two-digit months October, November, December (10, 11, 12) may only have single digit dates, so those three months include 3x9 or 27 possible dates.
April, June, September may end in a number no higher than 30, which adds 3x30 or 90 dates.
January, March, May, July, August may end in a number no higher than 31, which adds 5x31 or 155 dates.
February (assuming not a leap year) adds a possible 28 new dates, for a total of 27+90+155+28=300 dates which can be expressed with three digits.
Since we are looking for the odds of it happening AT LEAST ONCE, the easiest way to find this is to find the opposite odds--the odds that it WON'T happen at least once, which means it won't happen at all. The daily odds of the date NOT being drawn are 999/1000 for each drawing, and (999/1000)^2 for two daily drawings, which is 998001/1000000 (0.998001as decimal) chance that the date will not be drawn on any given day.
Now we take the odds that it won't happen on ONE day and raise that to the 300th power: .998001^300. Subtract this answer from 1.0 to get the odds that it WILL happen at least once those 300 drawings. This rounds to .548647, so the odds of it happening at least once become .451353. Pretty close to a 50-50 chance of NYC's drawing matching at least one date, in any given year (not counting the impossible dates).
However, this is just one local drawing. Keep in mind there are such drawings all over the country. We don't know exactly how many, but, just to get an idea of how fast the odds change when we take it outside of New York, suppose that each of the 50 states holds one such drawing. Now the odds of no current date being drawn anywhere in the country become .548647^50, which is .000000000000092, a verrrry small number. Subtracting this from 1.0 gives the odds of a current date being drawn at least once in a daily drawing of .999999999999908, just about a "sure thing." If the number had been drawn in San Diego or Chicago or Des Moines or Lexington or Miami folks would still be amazed, the number of amazed folks varying only according to how many heard about it.
Having ANY date drawn on its day is not so surprising. We just NOTICE it more when it's a significant date. How many dates are that significant that anyone would notice? Surely just a few a year, so it seems far less probable to have a day's date drawn than it actually is.
Our reaction to such things tends to be based more on emotions than statistics. The SIGNIFICANCE of a number drawn cannot be measured mathematically, so we can't factor "significance" into our statistical equations. Significance is an illusion created by our own emotions. So I guess I have to agree with DJ and her husband on this one.
Last edited by pstewart; 09-30-2002 at 06:42 PM.
How about this answer??!! I just heard on the radio yesterday, that some heads at Princeton, I believe, have an explanation for this occurance. They insist that it is an example of psychokinesis. They believe that so many people, thought of 911 so often that day, that the psychokinetic energy actually caused the number to come up! I swear I am not making this up. I guess this is why they get the big bucks.
Now I would like everyone on this site to channel all their psychokinetic or just psychotic energy to me.
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