Deed Recorder probibility question (or "too much time on our hands on a friday afternoon")

As most of you know, I work as an abstractor for gas well titles. What you may not know is that this job can lead to a lot of "counter time" waiting for photocopies to be made and thus a lot of "counter talk" with the guys making the copies. Today I had two such discussions, partly based on neither me nor the guy making the copies really wanted to do much more work after 3:00 on a friday. So anyways, the two questions.

Question 1 revolved around probability of having a deed recorded at "Page 1" vs any other page. Since I assume most people are not very familiar with this, a little on how deed recording works....

Before around 2000, deeds in most places were recorded in "Deed Book." Way back in the 1700s or before, when the USA was first being settled, people knew we had to keep track of who owned land, as they had done in Europe where they left from. Somebody very organized and with good handwriting got appointed or elected "recorder of deeds." Someone sells a property, say Wizard sells a lot to EvanBob. They write a deed and go to the county to show it on record. The "recorder" copied it all, word for word, in his book. When he recorded it he would assign it a "page" number. Say these two made the first deal ever, so it went on "Book 1, Page 1." Years later, EvenBob decides to sell to FleaStiff. So when they write that deed they must "recite" how EB got the property, in most cases this is the form of saying, "being the same property EvenBob acquired from Wizard and recorded at Book 1, Page 1." Then a book and page is assigned for that deed. Most decent-sized counties in the East have from a few thousand to over 15,000 "books" with all these recordings. In the late 1990s many places stopped using physical "books" in favor of computer storage. At the same time, many stopped issuing "book/page" and just gave an individual file or doccument number. So that is the background.

Where I am at most books have 750 pages, with maybe a few less or more based on the last deed being a page or two short or long. Deeds do not start at the "top" of a page. IOW, if 1/4 of the way down one deed stops, they leave a few lines of white space and start another one. Here is where the conversation came in. My deed was on page 1 of a book. The guy at the counter said he sees that. I said "It should actually be a higher probability because page 1 is the only page a deed HAS to start. (as we all know, you just notice it more.) He agreed but we had no idea to figure how much the probability would be. So here are the parameters for the better-than-AZ-at-math guys:


Books are 750 pages, no deed will start on page 750 if it will not finish on page 750 (see deed legnths below)
Deeds records start on page 1 (ie: no "cover" pages, etc. at least one deed MUST appear at page 1)
Deeds can start on page 749 and spill over with no restriction on the deed spilling over (ie: 2 pages or 10 or more as long as it starts it records at 749)

As to deed legnth, here is where it gets hard and I realize it makes all the difference. So a little guessing.

50% of deeds are between 1.34 and 1.68 pages in legnth with all 50% evenly distributed over that range.
10% are .34 pages long
30% are 1.69 to 2.5 pages long with the entire 30% evenly distributed over that range
10% are a random legnth up to 10 pages with it being less and less likely to be longer as the legnth increases. Meaning a 4 pager will be more rare than a 3 pager and a 5 pager more rare than a 4 pager.

Now, after all that, how would one figure the probability for any given page? What is the probability of getting a deed recorded at page 1? What is the most probable page? The least?



BONUS QUESTION: the guy, when I told him of this board, told me to ask how many seconds there are in a day. It sounds like a trap as it should be 60 * 60 * 24. What am I missing?

Quote: AZDuffman

BONUS QUESTION: the guy, when I told him of this board, told me to ask how many seconds there are in a day. It sounds like a trap as it should be 60 * 60 * 24. What am I missing?

Ask a few questions first:
1) On what planet?
2) Using what definition of "day" (sidereal or solar)?
3) On what day of the year?

The length of an average sidereal day, or the period of time when a fixed point on Earth is facing exactly the same absolute direction as it was "yesterday", is about 23 hours and 56 minutes. The normal definition of "day" is when the fixed point on Earth is facing the sun, but since the Earth is revolving around the Sun in the same direction it rotates, it actually has to rotate *past* the same absolute direction to point at the sun again. That's a "solar day", what is commonly defined as 24 hours. Except even then that's just an average because the (a) the orbit of the Earth isn't circular and (b) the Earth is rotating on an axis relative to its orbital plane. So a solar day (between noon one day and noon the next) can vary as much as 30 seconds depending on when you measure it.

But if he's not trying to trick you, it's 60 * 60 * 24. :)

Quote: MathExtremist

Ask a few questions first:
1) On what planet?
2) Using what definition of "day" (sidereal or solar)?
3) On what day of the year?

But if he's not trying to trick you, it's 60 * 60 * 24. :)

I said it was 60*60*24 but he kind of acted like he didn't get it. I don't push stuff there as while the guys are cool to us it is a bit like the airline desk agent--they can help you or make your life harder.

"I said it was 60*60*24 but he kind of acted like he didn't get it"
LOL Maybe he was really asking #1 - Alien disguised as paralegal.