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Thread: Statistician or Math Whiz help

  1. #1
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    Default Statistician or Math Whiz help

    This has to do with the standard Indiana license plate that most auto have.

    For those not familiar with the plate, the format is something like this.....

    99 A 1234

    2 numbers followed by a letter followed by up to 4 numbers.

    I tend to notice plates on my way to & from work each day. Recently on my way home the car in front of me had a plate kind of like this one......

    49 G 2327 - I couldn't tell you the type of car that is was, doesn't really matter. Thats not even the "exact" number. but for this question, its close enough.

    Anyway, heres the odd part.

    I looked though the windows of that car to look at the plate of the car just ahead of it. That car was completely different & once again, I have no clue what type it was. However the plate was very similar.

    The first 2 numbers were different, the letter was different as well. However the last 4 numbers were next in sequence. Something like 99 Z 2328.

    Heres the problem that I have for you.

    What are the odds of seeing two completely different make & models of autos together like that, with the last 4 numbers being in sequence?

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    Default Re: Statistician or Math Whiz help

    Where are C3PO or Mr. Spock when you need them?

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    Default Re: Statistician or Math Whiz help

    I'll take a stab at it and say...

    very, very small.

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    Default Re: Statistician or Math Whiz help

    What in the hell

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    Default Re: Statistician or Math Whiz help

    Quote Originally Posted by Jose Slaughter View Post
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    What are the odds of seeing two completely different make & models of autos together like that, with the last 4 numbers being in sequence?
    I would guess 1 in 10,000.
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    Default Re: Statistician or Math Whiz help

    Practically seen you're right, Kat. But to be entirely correct.....

    There are 10000 possible sequences for the last 4 numbers (0 - 9999). But there are more than 10000 cars in Indiana. So there are some plates that end with the same 4 numbers.

    However, unless you work for the license plating service, you can't possibly know how many plates have a certain 4 number sequence. Therefore, let's assume a random distribution: on average, every ending 4 number sequence is used a same number of times. How do we calculate that number?

    Easy, we just have to know the number of cars in Indiana. Let's call this N. Then the average number will be N divided by 10000. Let's call this average number A.

    Now we're in business. Pick a random car. Then there N-1 cars left. Out of those N-1, A will have the follow-up 4 number sequence. Thus the chance is A to N-1, or N/(N-1) to 10000.

    So the chance will be a tiny bit higher than 1 to 10000. Of course, N is an extremely large number (10 million or so), which makes N/(N-1) very, very close to 1. A result of 1 to 10000 is thus more than good enough.

    That's a pretty rare event you witnessed there, Jose

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    Default Re: Statistician or Math Whiz help

    It just occurred to me that (roughly) 2 in 10,000 is more accurate since the second vehicle could have the number just above or below the first vehicle, as long as the first vehicle doesn't have 0000 or 9999.
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    Default Re: Statistician or Math Whiz help

    Do you need to factor in the fact that the cars were together at the same spot at the same time?

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    Default Re: Statistician or Math Whiz help

    Quote Originally Posted by Kat View Post
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    It just occurred to me that (roughly) 2 in 10,000 is more accurate since the second vehicle could have the number just above or below the first vehicle, as long as the first vehicle doesn't have 0000 or 9999.
    Yeah, you're right, didn't think of that

    Quote Originally Posted by Jose Slaughter View Post
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    Do you need to factor in the fact that the cars were together at the same spot at the same time?
    Well, you kind of do, I think, by randomly picking two cars out of the whole bunch. Statistically seen, that method represents "same place at the same time" very well if there is no geographical bias (for instance, numbers 0 to 4999 in the north, and numbers 5000 to 10000 in the south) in the allocation of license plates.
    Last edited by Raskolnikov; 06-08-2007 at 12:01 PM.

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    Default Re: Statistician or Math Whiz help

    Well the first two digits in the licencse plate code is the county number. 49 is hamilton and 99 is marion if I'm not mistaken. So the fact that both of those arte next to each other, probably would bring that statisical reference for them being near each other down a little. But still, marion and hamiltons counties are not exactly small......

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    Default Re: Statistician or Math Whiz help

    Quote Originally Posted by SycamoreKen View Post
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    Where are C3PO or Mr. Spock when you need them?

    The odds are approximately 3720 to 1.
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    Default Re: Statistician or Math Whiz help

    All I know is that once I graduated Finite mathematics I swore to never deal with said calculations again. It certainly sounds like Permutations and Computations and I hate those.
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    Default Re: Statistician or Math Whiz help

    A LOT more likely than you might think.

    1.
    First, 1 or 2 in 10k would refer to finding a "match" given a specific number, i.e. I see 2327, what are the odds of seeing either 2326 or 2328? It doesn't address seeing some other number and then figuring the odds of matching that one. Or seeing a third number and matching that. I ain't doin' the math.

    2.
    This is a similar question to how many people in the room have the same birthday? It turns out that the odds of two people having the same birthday are about 50% when there are 23 people in the room. No I ain't doing the math for you. It's true, just accept it and move on. If you cause a stink I WILL do the math, and insult you at the same time.

    3.
    Each county could easily have a 2327 with its own county prefix added, so that changes the odds, but not very much since it means that car from the other county has to be traveling in your county at that moment. Also some counties, like Marion, have more than one prefix so there may be multiple 2327s in the same county.

    4.
    When I've gone downtown to meet my wife for dinner after work and we're both driving back home, our license plates are consecutive. If we went to work at the same time in the same direction, there ya go again.
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    Default Re: Statistician or Math Whiz help

    Quote Originally Posted by Knucklehead Warrior View Post
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    A LOT more likely than you might think.

    1.
    First, 1 or 2 in 10k would refer to finding a "match" given a specific number, i.e. I see 2327, what are the odds of seeing either 2326 or 2328? It doesn't address seeing some other number and then figuring the odds of matching that one. Or seeing a third number and matching that. I ain't doin' the math.

    2.
    This is a similar question to how many people in the room have the same birthday? It turns out that the odds of two people having the same birthday are about 50% when there are 23 people in the room. No I ain't doing the math for you. It's true, just accept it and move on. If you cause a stink I WILL do the math, and insult you at the same time.

    3.
    Each county could easily have a 2327 with its own county prefix added, so that changes the odds, but not very much since it means that car from the other county has to be traveling in your county at that moment. Also some counties, like Marion, have more than one prefix so there may be multiple 2327s in the same county.

    4.
    When I've gone downtown to meet my wife for dinner after work and we're both driving back home, our license plates are consecutive. If we went to work at the same time in the same direction, there ya go again.
    5.
    You have to account for specialty plates and truck plates as well.
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