What are the odds of this happening?

[dcarr]

Just to add to the conversation. I play NY's pick 3 and know that those particular numbers have not been drawn since before 9/11/01! Even since we went to 2 drawings per day. I did not play those numbers that day, but I do know about 5 people who did. 4 don't know what to say and 1 couldn't care one way or the other. People often stun me.
Debbie

[dcarr]

Forgot to add this. I, too, think it's fishy. And if it was a rigged situation, then it was in very bad taste.
Debbie

[clausiam]

Better late than never. Just happened to look at this old thread and as I have a minor in math - mostly forgotten but some probability theory still sticks - I thought I'd post this:

The odds are in fact: 0.001999 or 0.1999% which is very close to 1 in 500 (0.2%) but not quite.

There were 2 drawings, each of them had a 0.001 (1 in 1000) chance of ending with these numbers as everybody agreed on. That means that for these numbers NOT to come out that day both drawings have to "fail" which they each had a 0.999 chance of doing. So the likelihood of both of them "failing" is 0.999*0.999=0.998001. Reversely the chance of at least of them succeeding in getting these numbers is then 1-0.998001 or 0.001999.

Things like this work almost linear in the low end (i.e. a small number of drawings where each has a small likelihood of "succeeding") which is why the 1 in 500 approximation is quite good (1 in a 1000 and then 1 in a 1000 is ALMOST 2 in a 1000, i.e. 1 in 500). However the "ALMOST" becomes important as you add more samples. As someone mentioned doing 1000 drawings would not make it certain that the numbers would come out of course. In fact the likelihood is smaller than you might expect at 1-0.999^1000 ~ 63%.

Sheesh, that was long

/Claus

[Ed_L]

Thank you Claus. Now I can sleep again knowing that I was at least in the ballpark.

Ed

[DJ Dubovsky]

Ah yes, when in doubt seek out a mathmatician. Guaranteed to confuse you even more than you were before. Sorry Claus, I actually thought it was an excellent explaination and the fact that it flew right over my head proves that.

I guess it boils down to no matter how bad I want to stick those other elements into the equation it just don't change the facts. I concede to those who know more than I on this subject which just about includes the entire world population.
DJ

[G. Couch]

Thanks Claus! Your avatar fits well! Seriously...thanks for the explanation!

[pstewart]

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.

Phyllis

[dcarr]

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.
Thank you
Debbie

[G. Couch]

psychokinetic icon...