# Any experts in statistics around? Something weird happened and I'm curious if the odds could even be estimated.

#### Funkworks

##### Low Earth Orbit, obstructing Earth's view of Venus
All you know for sure is the probability is something less than 1 in ABCDEF. ;-)
I might be taking this too seriously but I don't agree. A model depends on when exactly you start the game, and what is known beforehand.

#### cls

##### Well-Known Member
You could also say that there was a 1 in 100,000 chance of having ABCDEF on the odometer,
ABCDEF is 6 digits, so zero through 999,999, one million possibilities. Not 100 thousand.

#### Rob Campbell

##### Well-Known Member
TRF Supporter
It happened, therefore, the odds of it occurring were 100%,

#### hobie1dog

##### Subaholic
TRF Supporter
Since high school I keep seeing the number 711 everywhere, multiple times each week looking at clocks, # of posts on forums, my son's first house 711, it just won't escape me. Now people into numerology say that it's a sign that everything in your life is going perfectly aligned. Talk about a crock of horse manure. Nothing could be farther from the truth. I'd like to go back and change 90% of my life starting before birth. It's just sheer coincidence, nothing more.

#### ThirstyBarbarian

##### Well-Known Member
I had an odd probability thing come up recently. I was writing up the results of a company step contest. In the results email, we include the names and step counts of the 10 prize winners who win a raffle, and we also include the names and step counts of the top ten people who log the most steps in the contest.

Rarely do step counts come out to an even 100 or 1,000. Usually it’s a largish number that ends in any random digits, not 00 or 000. but this time there was one participant who had a step count of exactly 415,000. Just having a step count like that is kind of an odd occurrence. To make it even odder, the person also was in the top ten, so they got recognized in the company-wide email, and odder still, they won a raffle prize, so they were mentioned twice.

#### ThirstyBarbarian

##### Well-Known Member
Since high school I keep seeing the number 711 everywhere, multiple times each week looking at clocks, # of posts on forums, my son's first house 711, it just won't escape me. Now people into numerology say that it's a sign that everything in your life is going perfectly aligned. Talk about a crock of horse manure. Nothing could be farther from the truth. I'd like to go back and change 90% of my life starting before birth. It's just sheer coincidence, nothing more.

Maybe you were meant to live in a 7-11 24/7.

#### Funkworks

##### Low Earth Orbit, obstructing Earth's view of Venus
ABCDEF is 6 digits, so zero through 999,999, one million possibilities. Not 100 thousand.
I purposely neglected cars having less than 100,000 miles because we know the number has 6 digits (not 5). And I purposely neglected cars with over 200,000 miles because there are much less of them. This was just to get a round number (100,000). Of course you could stretch the range to be from 100,000 to 300,000 instead, giving a range of 200,000 possibilities. But frankly, the probability of a car having anywhere between 300,000 and 999,999 miles is negligeable IMO.

A more accurate model with 100,000 possibilities is to consider that a weight curve for car mileage has a peak at around 178,000 miles. So sticking with 100,000 possibilities around 178,000 is close enough for me (a bell curve centered on 178,000 ± 50,000).

Either way, 100,000 possibilities is a round number with ok accuracy. If you want to consider a wider range, you'd have to account for weights (how many cars in the US for each value of mileage). Not sure it's worth it for this thread.

Basically, imagine a bell curve centered on 178,000 miles, and trim off the tails. Then, square it off to make a rectangle centered on 178,000. Now you have an equal probability for each possibility between 128,000 and 238,000 miles. Chances are the powerball number is in there, and you have 1 chance in 100,000 to get it.

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#### 75Grandville

##### Well-Known Member
TRF Supporter
Speaking as a statistician (I knew all those years in college would help), let's do a thought experiment.

Assuming that you got the sticker at mileage A(B-1)CDEF, you've got a range of 10,000 to play with to observe the match. For now discounting possibility of going over.

Then there is the rate of checking the odometer. Let's assume that on average you check every 1,000 miles - an infrequent event, with a uniform distribution.

So the probability works out to something like 1/1,000.

Like any other probability calculated from assumptions, the estimate is only as good as the accuracy of the assumptions.

#### Funkworks

##### Low Earth Orbit, obstructing Earth's view of Venus
Assuming that you got the sticker at mileage A(B-1)CDEF, you've got a range of 10,000 to play with to observe the match. For now discounting possibility of going over.

Then there is the rate of checking the odometer. Let's assume that on average you check every 1,000 miles - an infrequent event, with a uniform distribution.
Yeah, that's the kind of knowledge that improves the model if you have it!

#### 75Grandville

##### Well-Known Member
TRF Supporter
Yep. But you have to start somewhere. The first assumption seems pretty reasonable. The second one, well, I have a colleague that remarks "80% of statistics are made up on the spot." It does provide a reasonable starting point.

#### KenECoyote

##### Well-Known Member
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Glitch in the Matrix!

#### Ronz Rocketz

##### NAR# 109557
TRF Supporter
It's not hard. 1 in 5. Now I'm pouting.

#### ThirstyBarbarian

##### Well-Known Member
Well, this coincidence was either going to happen or it wasn’t, so it sounds like the odds were fiddy-fiddy.

#### ThirstyBarbarian

##### Well-Known Member
I read once about these kinds of mind-bendingly unlikely coincidences and how they happen more frequently than you expect. And it’s because there are far more impossible-seeming coincidences that could potentially happen than you think. You just don’t think about them until they actually do happen, and then it seems so bizarre. But there are millions of equally bizarre coincidences that could potentially happen every single day but don’t.

Basically, something weird is bound to happen eventually, but you just don’t know what. It may seem like a one-in-a-million event when it happens, and maybe that one specific event is actually that rare, but it’s not rare for random rare things to occur.

#### cls

##### Well-Known Member
So sticking with 100,000 possibilities around 178,000 is close enough for me (a bell curve centered on 178,000 ± 50,000).
As you noted, a diminishing probability of 300k to 999k.

Looks more like a Poisson distribution, perhaps peaked at 178k, or so.

#### ThirstyBarbarian

##### Well-Known Member
Here’s another weird coincidence that happened to me a couple years ago. I gave a stranger begging for money a \$5 bill in a Target parking lot when I was out running errands. About an hour later I was out for a walk in my neighborhood and found a \$5 bill on the sidewalk.

Weird.

It might not be too uncommon to give a stranger some money, but it is pretty rare for me. I don’t live somewhere where I get asked very often — maybe a couple times a year at most — and I don’t always do it when asked. Also, it’s not unheard of to find money on the ground, but it’s rare enough I think I can remember most of the handful of times it’s happened. So what are the odds I’m going to give away \$5 and then find that exact amount on the ground an hour later?

#### jderimig

##### Well-Known Member
Assuming the odometer is below the number on the sticker at one point and you are the only driver of the vehicle.

Q. What is the probability of the odometer matching the sticker at some point?
Q. What is the probability of you being behind the wheel when this occurs?
Q. What is your time average speed?
Answer: Probably less than 15mph or 4 minutes per mile to observe the match.

Apply the probability of random events doesn't work here. This is not a random process.

The probability of this OP event is higher than most are estimating here.

#### cls

##### Well-Known Member
Here’s another weird coincidence that happened to me a couple years ago. I gave a stranger begging for money a \$5 bill in a Target parking lot when I was out running errands. About an hour later I was out for a walk in my neighborhood and found a \$5 bill on the sidewalk.
A few years ago... Dropped off my old truck at the local shell station. The mechanic said he'd look at it. Symptom was chugging on startup, pro6loose +12v from the relay to the starter solenoid.

I walked over to get some take out Chinese food for lunch. Walking back to the station, past an ATM.. Big wad of bills on the concrete. Grabbed them. Looked around. No one there. Am I on Candid Camera? No?

Went back to Shell station. The mechanic was mad at me because the truck had a Speedee Lube oil change sticker in the windshield corner. He said he would have given me at better beal for the starter repair if I got regular oil changes from him. I said, you're too good for that.

He said it was the crimp connector, so \$60! I pulled the wad of bills out of my pocket and said here, this'll do ya.

It might have been 5 or 5 6 \$20s but he always did a great job on the truck after that.

#### ThirstyBarbarian

##### Well-Known Member
I still think the odometer thing is a very unlikely coincidence. I don’t think it lends itself well to analysis because of a lot of different factors. But as described, Sandy only thought about the oil change because of an upcoming road trip, checked the odometer at that moment, and then checked the sticker and saw the match. No matter what analysis you use, it starts with that one narrow window of a match — one mile out of the possible miles driven, or a minute or two out of the hours driven. The other piece of the puzzle is the thing that prompted Sandy to check if it’s time for an oil change. In this case, it’s going out of town. Some people might have a more formalized method for oil changes, like every 3 months or 6 months or whatever. Or some people might monitor or record their mileage. In those cases, you might happen to check at about the right time, but even then, it seems unlikely you would check at the exact moment that the mileage matched the sticker, unless you were really looking for it. And that doesn’t seem to be the case for Sandy. So the idea that an upcoming road trip might remind someone it might be good to check if it’s time for an oil change, and then that be the exact moment the mileage matches the sticker? That’s pretty far out.

#### jderimig

##### Well-Known Member
But as described, Sandy only thought about the oil change because of an upcoming road trip, checked the odometer at that moment, and then checked the sticker and saw the match. No matter what analysis you use, it starts with that one narrow window of a match —
Beating my random dead horse here...

The number on the sticker is not random. It is a constant and is stored in Sandy's brain.

The odometer is not random. It's incrementing and predictable. That number is also in Sandy's brain along with an estimator predictor that is probably very good.

Why did Sandy's brain think about an oil change at that particular moment? What was the stimulus for that? Was that random or was Sandy's brain subconsciously drawing a convergence on its sticker number and its odometer model? Randomness is rare. Something to think about...

The brain is a calculator. Free will is a myth.

#### Sandy H.

##### Well-Known Member
TRF Supporter
I'm not going to quote specific replies, as I'm not trying to support or refute any of the statements made. I am appreciative of all of the different views and agree with some of the scenarios (some more than others). I agree the method would be to state the assumptions and then perform the math based on those assumptions. In my opinion, the assumption related to time is the real kicker. I know the conditions at the moment the observation was made (i.e. 45mph on Monday around 1:50pm) and that the condition was only true for roughly 1min20sec. That FEELS like a very important part of the equation and makes me FEEL like that is the random event aspect, especially given how rarely I look at the odometer [side bar: I probably looked at the odometer every minute or two that I was driving since yesterday. . . lol].

So far, I think the proposed bounds are between 1/1000 and 10/10e9.

#### Grog6

##### Well-Known Member
TRF Supporter
Talking about probability; one of the parts of designing electronics is reliability. My oldest car, a 1996 Mercury Cougar, is at over 500k miles on the odometer. It has developed a rod knock, telling me it needs some attention. My family doesn't understand reliability; all the surviving components of the car are far into the "Bathtub" part of the curve; the main failure mechanism now is wearout of components. I plan to replace the bearings, inspect everything,replace other wear items, do any machining that needs done, and drive it another 500kmi, lol.
I've spent 86k dollars, driving those 500k miles, so it comes to 0.17 dollars per mile. so adding the \$500 for the rebuild stuff, and it makes it 0.173 per mile

#### Sandy H.

##### Well-Known Member
TRF Supporter
Beating my random dead horse here...

The number on the sticker is not random. It is a constant and is stored in Sandy's brain.

The odometer is not random. It's incrementing and predictable. That number is also in Sandy's brain along with an estimator predictor that is probably very good.

Why did Sandy's brain think about an oil change at that particular moment? What was the stimulus for that? Was that random or was Sandy's brain subconsciously drawing a convergence on its sticker number and its odometer model? Randomness is rare. Something to think about...

The brain is a calculator. Free will is a myth.

I can answer a few things.

I really don't think I consciously looked at the sticker at any point. I may have just due to visual observations, but I really and truly would have expected it to be a Shamrock sticker at around 101k, not a Scott Clark sticker at 123k. It turns out my wife was the one that took the truck in when I was out of town, so I didn't even participate in the event, which makes sense why I expected it to be way over. This is actually a positive for me, as I was afraid I was losing my mind. . .

Why did I think about an oil change? It is 100% (IMO) related to the fact that I am getting ready to take a 1500 mile road trip and that I need to check tire pressures, clean the truck etc. before doing that. If my truck breaks-down in my daily life, it is a 30 minute inconvenience in general, but I was raised by example to make sure you know the state of your vehicle before going places you've never been and/or are far away. I had, in my head, the memory that I was probably 10k over on mileage for an oil change and was going through, in my head, the list of stuff I had to do before leaving tomorrow. The fact (and it is a fact) that I kind-of don't care about being a few thousand miles over on oil changes since factory says 10k oil change period and I had them change oil at a 5k interval for the first 100k, because I never paid attention (i.e. I was still thinking the 3k rule and synthetic is 5k - never checked the manual), I'm not an odometer watcher for sure. The truck has a separate display for miles until empty etc., that is nowhere near the odometer, but I do watch it often.

Based on the fact that these observations did not make me 168 million dollars richer based on the odometer reading and relating them to the PowerBall drawing, I agree that the brain sees a ton of stuff that it chooses to discard instead of storing and I'm pretty sure that is the base definition of the scientific method: Sandy observed one event and therefore, that is how the human brain works.

Still impressed the discussion is going on, honestly. Usually by now we'd be talking about glue. . .

Y'all are awesome and I hope it continues, as I personally am leaning toward the 1/10e9 order of magnitude myself, but will gladly listen to every premise for 1/10 to 1/10e999.

#### Grog6

##### Well-Known Member
TRF Supporter
What glue is used to attach a coconut to an african sparrow? Asking for a friend...

#### ThirstyBarbarian

##### Well-Known Member
Beating my random dead horse here...

The number on the sticker is not random. It is a constant and is stored in Sandy's brain.

The odometer is not random. It's incrementing and predictable. That number is also in Sandy's brain along with an estimator predictor that is probably very good.

Why did Sandy's brain think about an oil change at that particular moment? What was the stimulus for that? Was that random or was Sandy's brain subconsciously drawing a convergence on its sticker number and its odometer model? Randomness is rare. Something to think about...

The brain is a calculator. Free will is a myth.

I don’t buy the subconscious explanation. The stimulus was going out of town, which is often the only reason I think to get my oil changed or do other maintenance, especially on my older cars. I have no idea what the mileage number on my sticker for my next oil change is, and I also have no idea what my odometer reading is on either of my cars. It’s not something I pay attention to or check unless I have a specific reason to look at it.

#### Sandy H.

##### Well-Known Member
TRF Supporter
What glue is used to attach a coconut to an african sparrow? Asking for a friend...
Pretty similar to the glue used to attach a coconut to an African swallow, I'd assume. Tightbond 2.

#### hobie1dog

##### Subaholic
TRF Supporter
I just want you to win the lotto.

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