Yesterday, in my random change received from purchases, I found a 1919s wheat back penny. 1919-s-wheat-penny/


1) What is the probability that I would receive this penny in change almost 100 years after it was coined?


2) What is the probability that I would receive on any given day After the occurrence above; that I would receive another 1919s wheat back penny?


3) Show all your work and needed assumptions to calculate the probability. This is an excellent exercise. You may learn something trying to sort out all the parameters and how to calculated a reasonable answer.

The correct approach is to imagine that you have made infinitely many purchases, and consider the proportion of times you get a 1919 wheat back penny. This is completely standard in probability theory.

Too many unknown and variables affecting this that are very difficult to put together confidently fast. You could however imagine a toy game that there are N total coins and n special ones and you are making a number of transactions every day that result in change 1,2,3,4 mod 5 probably with the same probability each and you also pay similarly some fraction of the time giving back coins and there is mixing in the coins etc and similarly for other people.

In reality people travel, there is diffusion etc and the chance it remains in the area is significant given if its 1 in a billion type coin and its always there and people do not collect it out of the circulation.

People that deal with cash probably get the same twenty many times a year i imagine.

Assuming we're talking about the normal 1919s and not ones with errors.

https://coinsite.com/how-many-us-pen...t-circulation/
Jack F. asks: How many US pennies are in current circulation?

A few hundred billion. Between about 4 billion and 8 billion cents are struck each year and though most are sitting in “penny jars” they are primarily used for paying sales tax.
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http://cointrackers.com/coins/13527/1919-s-wheat-penny/

Type: Wheat Penny
Year: 1919
Mint Mark: S
Face Value: 0.01 USD
Total Produced: 139,760,000 [?]
Silver Content: 0%
Numismatic Value: 35 cents to $475.00
Value: As a rough estimate of this coins value you can assume this coin in average condition will be valued at somewhere around 35 cents, while one in certified mint state (MS+) condition could bring as much as $475 at auction.
================

Between pennies going into jars over the past 100 years and collectors who look for ones with numismatic value like the 1919s, I doubt there's even 1000 left in circulation. Adjust chances below according to your guess on this.



Let's say you got 3 pennies in your change and there's 300 billion in circulation. Then I'd say the chance one of them was a 1919s is less than 1 in 100,000,000.


On a par with winning Megabucks.



PairTheBoard

Thinking about it some more, they are saying that pennies sitting in jars count as "in circulation" and make up the majority of pennies "in circulation". I'm thinking of what we might call, "active circulation", i.e. not sitting in jars but actually circulating. Maybe there's only 100 billion pennies in active circulation. Then the probability above would be 3 time greater, or about 1 in 33 million.

I collected pennies as a kid and looked through a lot of rolls of pennies. It was a good day if I found one 30 years old. A special day if I found one 40 years old. Once or twice I found one 50 years old. I never came close to finding one 100 years old.




PairTheBoard

Most dormant coin collections get back into circulation when the owner dies and the inheritors do not care, or do not know the value of the coins. This would lead to a increase in circulation around the time that coin collectors reach the late 70’s in age.

The hobby was popular among teens into the 60’s, so the age group can be considered to have a lower bound of persons born around 1950, so collections have been appearing and should continue for another decade. After that, it should drop off considerably.

My Dad (born in 1951) loved collecting coins. I received his 1909 SVDB cent, in mid-high grade with wonderful color streak in the copper.

I also collected coins as a kid. Still have a few of them.


Years ago, about the mid-1990's, I got a buffalo head nickel in winning change at an old style slot machine in downtown Vegas. It was very, very worn but still easy to identify. Must have been circulating in Vegas for years and years but it was a surprise to me to get one. I thought then about the probability of receiving a certain type of coin (older, rare or otherwise) either in random change or other means (winning at coin dispensing machine).


Based on a quick search 100 to 200 billion pennies in circulation seems a reasonable estimate. PTB's adjusted number appears to be in the ballpark.


The point about people spending or putting back into circulation coins that are old or rare or from previous collections is a good one. This would up the probability in a locally prescribe area where such a 'mistake' is made.

I collected coins too, kind of always have, looking at the coins, putting interesting ones aside. That's history now, switched to plastic money quite recently.

Glad you are keeping up the flag, Zeno.

Ho! (to quote Bertie Wooster). I'm not buying any of the above. It appears lame and an excuse to dodge hard work and thinking. I know that PTB's estimate can be improved upon. I suggest you head to the local pub and down a few pints and get out a crayon and table napkin and start calculating and conjuring some equations. For example: A/b X a/B X y/x X M/N (n-1) given assumptions, e, f, g, etc and so on. British pride is at stake!

The correct answer is that the probability is zero. That doesn't mean it cannot occur. Like when you flip a coin an infinite number of times, an event with probability zero occurs. Again, totally standard.

The above sounds almost, well, biblical. Mathematicians have taken a tumble in my esteem if the above is true and "standard". Zero is not a number. I demand a number.

There is obviously a proof of your above assertion, if standard. It probably reads like the book of Revelations, I'm guessing. Send me the link and I'll read it in the bar tonight. Thanks.

Of course there's a proof. It's called Appealing to Authority.

You didn't find the coin, it found you.

Since every coin Zeno has ever examined in change was not a 1919s, except the one time, then would not Bayes agree that there is no reason to think it will ever happen again?

Or, can we play more loosely and look for any coin with numismatic value, and then guestimate the likelihood it is 1919s?

Eyeballing a wheat penny is pretty easy, we all have done it many times, and this should get some actionable stats beyond “zero durrr”.

I mean, coins wear out and get replaced when they fail a test at a Federal bank, iirc. Older coins that are different than the newest coins get retired. Silver coins get recycled.

I would agree there is zero chance the 1919s was in circulation for 100 years, it would be so worn as to barely be recognizable as a penny, let alone a wheat with a readable 1919s designation.

So, when a collection gets recirculated, and any coin not in a sealed graded container is just loose change in a jar, how often will Zeno get one and how often will it be 1919s?

If most of these are worth around a dollar or two twenty years ago, they would just be in a jar from a collection over 20 years old. So, as a particular example of numismatic coins, not any less likely than most wheat pennies.

That's a damn good movie and an excellent answer.

Roughly the same as getting the first one, unless you think there are only a handful of them circulating, which may be the case.

The antagonist of our story is presented above. Robert was on a good track in thinking on acquiring the needed parameters for a better calculation/estimation. The unknown factors, and Bayesian mysteries are these:

1) Roughly four months ago a large coin collection was purloined from a local residence (I knew the people). It contain many old pennies including old Indian Head Pennies (IHP). IHPs are very distinctive, wheat back pennies (WBP) are not. I guarantee that at least one 1919s WBP was in that coin collection.

2) The criminal was/is an idiot but cognizant enough to not spend an IHP but ignorant or lazy when it came to WBP's or other coins that were not obviously worth a lot (like silver dollars). He is also a drug addict.


3) The area is rural with a settled population of say 2,000 people. The local small town has about 15 business but I frequent only 3 regularly: the main grocery store, the hardware store, and the bar. Almost assuredly I received that coin at one of those locations.


With these added titbits of information and using critical thinking skills and reasonable assumptions and parameters, I know a better and more actuate estimation of the probability of my receiving the said coin can be calculated. I know Masque could do it!

Depends on how many pennies you got in change and also on how many of them are still in circulation (i.e. not locked away in a collection or a sock or taken out by being destroyed/lost) with respect to total number of pennies currently in circulation.

But since you want an exact probabilit: it is 1 (since you did get it)

If you spent it in the meantine it's the same (actually a bit higher, since one of he coins - the one that you spent - is likely still in your vicinity so getting it back is more likely). If you didn't spend it it will be lower - again depending on the ratio mentioned in 1). Probably only marginally so in either case.
Pennies can sit on shelves or in jars for decades. A good fraction of them may not wear out if similarly 'static' - even after 100 years.

Based on 100B total circulation and 300M U.S. population, the town might have 666,000 pennies circulating in the town (seems high). One of those is the 1919s. If you got 3 pennies in your change the chance would be about 1 in 222,000 you'd get the 1919s. Quite a bit better than 1 in 30 million.


Chances would be better if you went shopping on national thief shopping day.


PairTheBoard

Very interesting. Possibly more tidbits of info available?

The idea of the coin finding you seems like a more organized way to navigate such a chaotic system of variables. View the variables from the pov of the coin.

Are we allowed to assume the coin is from the stolen collection? Since the probability that a 1919s found you otherwise is so remote that it can be stated as zero, then if we are allowed this assumption that is a big step, imo.

How many wheat back pennies were in the collection, estimated? Jars full, or in coin holders/binders? Maybe this is totally unknown.

What about the businesses you do not frequent? Do any of these establishments have semi-legal gambling machines? These exist in my rural community. This will decrease the likelihood since the coins deposited may stay in the machine for a very long time.

Does the main grocery store have a CoinStar or equivalent coin consolidation machine? This is likely where the coins were dumped, and the receipt can be used to buy food. From here the coins go to a local bank, in rolls, to await the needs of local businesses, such as bars, grocers, and hardware stores.

Is there a pawn shop? Loose coinage can be legally purchased without a waiting period, and this is not dealing in stolen goods in most jurisdictions since it is legal tender. These are gone forever from the local circulation.

How much publicity was there about the robbery 4 months ago? In a small town, everybody knows or nobody knows. Were multiple people eyeballing their change?

Now, since you are the one the coin found, how receptive are you to numismatic coins? Do you always check every coin? Have you increased your examination of coins since the robbery four months ago? Maybe this does not matter since it is not required for you to observe the coin for you to receive it in change.

So, the coin joins the local population somehow. It dodges all these obstacles and winds up in your pocket.

So maybe the chance is more like 1 in 2000.


PairTheBoard

Just a hair under 100%. The calculation is the sum of the probabilities of each event that would make you say "well, that is quite rare" over the time-period in question.

Much greater than the general odds of receiving such a penny, but far less than 100%. Either the owner of a jar full of old coins has died in the general vicinity and whoever was the beneficiary of the death has started spending them, or some enterprising lad has discovered that grandpa doesn't pay much attention to his jar of old coins and he traded some in for some candy or ice cream, or the same sort of thing with the coins in some other vessel.

Basically, it is highly unlikely that the sample of local coins in current circulation is even remotely representative of the population of coins circulating at this particular moment in time.


Edit: should have read the other responses

There must be some rule of thumb that if you find something rare, the probability of finding another increases.

According to data from these sites that we may need to review further for accuracy there were 590 mil 1919 pennies circulated and currently 1.65 tril total out there now and 140 mil type 1919s (lol 5000 per us citizen are you kidding me? who has it?) (imagine that i dont even have 30-40 total in some place at home as i consistently get rid of them when i pay with cash because they contribute to huge weight in wallet for nothing).


https://www.creditloan.com/blog/the-...n-circulation/
http://www.thewheatpenny.com/about-t...eat-penny/382/

"The 1919 penny is the most commonly available coin from the era. Three different mints produced nearly 590 million pennies in 1919. Many of these pennies are still in circulation today. 1919 pennies from the Philadelphia mint are most common. The Denver and San Francisco Mints produced smaller numbers of these pennies, which makes them harder to find."

https://www.reference.com/business-f...48e341f2ed103b

Apparently one should collect them and look at them for how old they are and put them in different stacks (if some are worth 30-40 times their value) although likely the time spent for this bs will be tremendous opportunity loss to make real money working on something decent and useful to society.

I have no idea and havent researched yet their rates of removal or how this works even to know how many are currently out there.

It is sensible to imagine that over the years people collect them in jars because they dont want to have them in wallets and never do anything about it so they outlive the owner.

If all of them were out there at any given point in time in active exchanging (and this likely is not true and could be described with some exponential decay function as people collect them in places they rarely reclaim from) then that means that there is 1 per 11800.

So if you have 30 of them at your home at any given point in time the chance one is from that era is roughly ignoring all fine modeling details;

(1-(11799/11800)^30~0.25%


So maybe its 0.025% if you take into account some gradual removal to jars over time say some factor 10 who knows.

This number could be way off if there is some major event that removed a lot of them or they look very different than the currently typical ones because if so i dont recall seeing anything different than the usual color ones all my life here. On the other hand definitely i havent yet seen 12000 ones or order that because i dont use cash like over 90% of the time i buy things.

The sad fact remains that the only purpose pennies serve in a wallet is to help not get more pennies into that wallet by paying with them when you owe something like 20.11 lol instead of giving some 20+1 or 2 20s. Sometimes the 10, 5s and 1s paper notes and quarters /dimes help (parking ) but you will get another 4 of the dark ones lol. Coin racism in action here lol.

The other purpose is the metal utility of their existence wherever needed in some unforeseen situation or the fact that with 3 of them you can play a game in a table. Start at one end of the table and pass one always between the other 2 (if you didnt manage you lose) until you score on the other side of the table in some fictitious goal post and you are only allowed to push them with your finger in one fast move one at a time. You start with the 2-1 reverse pyramid format. Games we once played didnt we?

However there is something dirty and dark about them that makes playing the same game with dimes or quarters superior lol. Sorry but this is a fact of life and you are not going to make me form some kind of empathy for pennies any time soon other than that once upon a time they could help put a smile in a child because you could get something with them. Maybe they can have that old memory of a time gone and remain proud in time.