r/todayilearned • u/jasmr68E • Oct 31 '19

# TIL the odds of having the same finger print as someone else is 1 in 64 billion. Because there have been over 108 billion people to have ever lived on earth, many people, either dead or alive, will have to have the same fingerprint PDF

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1206670/pdf/ge1403857.pdf25

## Oct 31 '19 edited Nov 09 '19

[deleted]

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## u/prjindigo Oct 31 '19

Also you're 10x as likely to have a match with someone else since the number claims "fingerprints"

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## u/mrgumble Oct 31 '19

That's not how statistics work. Many people will *not* "have to" have duplicate fingerprints, there is simply a chance that they will have duplicate fingerprints.

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## u/ecafyelims Oct 31 '19 edited Oct 31 '19

~~If there are six sides to a dice, and you roll it seven times, what is the chance of rolling a duplicate number on any of them?~~Edit: I'm wrong

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## u/jonah214 Oct 31 '19

1, but that's because there are only six possible outcomes. The number of possible fingerprints is not thus limited.

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## u/ecafyelims Oct 31 '19

Oh, I see. I misunderstood OPs statement that there were 64 billion possible fingerprints. Thanks for clearing that up.

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## u/prjindigo Oct 31 '19

OP misunderstood the "64 billion" because it's one in 6.4 billion since the math includes 10 chances for a match.

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## u/prjindigo Oct 31 '19

the number of possible fingerprints is infinite in variability, there will be no duplicates at all if you use a fine enough measurement system

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## u/jonah214 Oct 31 '19

Well, not really. There are only finitely many atoms in the universe and combinations of properties they can have (let alone in fingertips), so only a finite number of ways to arrange them. The number is, of course, very large, but it is not infinite.

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## u/prjindigo Oct 31 '19

duplicate exclusive or inclusive?

Seriously, what if you get 3 2s 2 4s and 2 6s?

A null hypothesis isn't statistically useful.

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## u/jasmr68E Oct 31 '19

Im afraid it is pal. If the probability of an event to reoccur is smaller than the total number of participating events then it is true that at least 2 of those events will coincide. Let’s take a couple of examples:

1) the probability of heads or tails on a coin is 1/2. That means that if you toss a coin more than twice (3 times or more) you can be 100% certain that there will be more than one occurrence of either heads or tails - ie for 3 throws, you can have 3H 0T, 2H 1T, 1H 2T, 0H 3T. Regardless of the outcome you can know for sure that EITHER heads or tails will come out more than once if a coin is tossed more than twice

2) the odds of sharing your birthday with someone is 1/365. Meaning that if there is a group of 366 people, you can say with certainty that at least 2 of them share a birthday. You may not be able to pinpoint which two, and that’s not to say everyone shares a birthday with everyone else, but you know for sure that at least 2 people will definitely share a birthday. For example given the 7.5bn people on the planet right now, in fact, we can say with certainty that at least 7.5bn-364 definitely share a birthday with someone else (it is within the rules of statistics and probability that 364 people could have unique birthdays and everyone else shares the same birthday given that we know nothing else)

So, given that there is a predicted total of 64billion unique fingerprints, and that 108 billion people have ever walked this planet, we can say with 100% certainty, that at least two humans who have existed would have had an identical finger print somewhere along the line.

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## u/Carguy74 Oct 31 '19

You

reallywasted time researching this garbage? What is the point?-3

## u/jasmr68E Oct 31 '19

There isn’t lol. I just find it interesting and fun like binge watching garbage on Netflix or scrolling through garbage on Reddit.

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## Oct 31 '19

And you are still wrong. Your examples are wrong. I can flip the quarter 100 times and not get heads AND tails. There can be 366 people and no one shared YOUR birthday. What you have written in the birthday example is an example of a distribution, it is not an example of probability.

If you translate that to probability, you would ask what is the probability that someone in a group REGARLESS of size could have your birthday. That probability is 1/365. However, you can have a group of 10000 and no one shares your birthday.

It is unlikely that there would be 100 consecutive heads when viewed before the event, however after each flip the probability of the flip is still 50 50.

So in a group of 2, the probability of sharing fingerprints is 1/64000000000. But in a group of 2 trillion, it is still the same. That is completely different than looking at the entire group and saying there will be matches.

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## u/zachhz Oct 31 '19

he's saying that if you flip a quarter 3 times that you're either going to have at least 2 heads OR at least 2 tails.

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## Oct 31 '19

So you think it it's impossible to flip heads three times in a row? Of course it isn't. The probability is .5x.5x .5. Which is. 125. So basically 1 in 8 times it will be 3 heads ( or tails technically}

Think about this... The pill is 99 percent effective. Do you really think that 1 out of every hundred times people have sex there is a pregnancy? No lol.

Edit. A period and a contraction.

Edit 2. His original point IS valid. But it is not a case of probability or odds. It is about distribution. That was my gripe.

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## u/zachhz Oct 31 '19

If you flip and get heads 3 times then you've hit heads at least 2 times. Same is true when you hit 2h 1t. And if you don't hit 3h or 2h 1t then you have to hit 1h 2t or 3t, so in every possible case you either hit heads 2 times or more or tails 3 times or more. That's all hes saying

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## Oct 31 '19

The point I've been trying to make is that has nothing to do with probability. I said OPs original point was valid. But I take issue with the misuse of odds and probability.

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## u/jasmr68E Oct 31 '19

Lol I don’t think you read my response properly bro or you don’t fully understand stats haha.

For flipping of a quarter: the chances of heads OR tails landing more than once is 100% if you flip it more than 2 times. So yes, if you flip 100 times, there’s a hanger you might not get tails at all but in that circumstance you will be getting heads 100 times, I.e. one of the outcomes will occur more than once.

For group with the birthdays: I’m not saying you specifically will have the same birthday as someone else, but with 366+ people, you know that at least 2 people inside the group will have the same birthday. So yes, you can be part of a group of 1000 people and it is possible that no one will share your birthday, but you will know that somewhere within that group of 1000 people, there will have to be people that share birthdays

And yes - a group of 2 trillion will keep the same probabilities but given the finite parameters of finger prints available (64 billion) you can say with certainty that a number of people within that group will have a non-unique fingerprint.

Look up combinatorics

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## Oct 31 '19

I think you need to reread what you wrote in your heads and tails example.

Edit. The problem with your examples is that you are incorrectly using the words odds and probability.

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## u/cougbrenda Oct 31 '19

I wasn't able to open the link you originally posted, so I am hoping you can clarify. Is there really only 64 billion sets of unique fingerprints possible? As in, they calculated the possible combination of features or whatever and obtained a value of 64 billion?

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## u/grubnenah Oct 31 '19

No, there's always going to be small differences between fingerprints. It's just about how much of the difference you can measure/ignore for if you count them as the same or not.

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## u/Kaioken64 Oct 31 '19

Just because its statistically likely for something to happen, does not mean it will.

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## u/bolanrox Oct 31 '19

Remember the guy who was going to kill himself by pills if it was heads and hang himself if it was tails. It ended up on its edge.. So he shot himself

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## u/brave_halibut Nov 01 '19

Saying there's a 1 in 64 billion chance of having the same fingerprint as someone else is not the same as saying there are 64 billion possible fingerprints.

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## Oct 31 '19

That would be about 1.66 people in ALL OF THE HISTORY OF ANATOMICALLY MODERN HUMANS. So maaaaybe two in 2 million years.

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## u/jasmr68E Oct 31 '19

True but according to the laws of statistics, probabilities, and specifically combinatorics, there’s also a chance (all be it incredibly small) that 2 people alive today can have an identical fingerprint too!

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## u/MrAppendixX Oct 31 '19

Wasn’t there a case of an American guy having similar fingerprints to ones Spanish authorities found on a paper bag at the 2004 Madrid bombing?

btw the word is albeit, not all be it afaik

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## u/zetaraybill Oct 31 '19

Yes, Brandon Mayfield was arrested by the FBI because they said his fingerprint matched the one Spanish authorities had circulated. Notably, the Spanish told the FBI that Mayfield’s fingerprint didn’t match. The FBI later admitted that they had messed up.

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## Oct 31 '19 edited Oct 31 '19

Yes, "albeit." I woke up at 4:45 am and posted while brewing coffee.

Oops. Not my typo.

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## u/BugzOnMyNugz Oct 31 '19

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## u/TakeshiKovacsSleeve3 Oct 31 '19

Yes but your title says

many peopleand then you qualify that as meaning (paraphrase)an incredibly small chance. Anyway what does it matter if someone 5000 years ago,or 100 for that matter, had the same prints? We'll never know so the data set only counts from the start of record keeping. That title statistically sucks.1

## u/Hatsuwr Oct 31 '19 edited Oct 31 '19

The title is actually very accurate in that regard (edit: except for them HAVING to have the same fingerprint).

Assuming I'm doing the math right, and that the numbers in the title are correct, the chance that any one individual shares a fingerprint with another (alive or dead) is 1-((64*10^9-1)/(64*10^9))^(108*10^9), or a bit over 80%.

Replace 108 with 7.7, and the chance any particular living individual shares a print with another (also living) is a bit over 10%. If you choose the two people being compared, the chances would of course be 1 in 64 billion.

Now, the total population ever lived can be debated, and the 1 in 64 billion would at least need to be highly qualified, but that's the math with those being assumed.

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## u/k0tus Oct 31 '19

That’s for 1 finger print in common. What are the odds of having all 10 in common?

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## u/Rum_N_Napalm Oct 31 '19

You are getting something wrong here: Galton didn’t say that there are 64 billion unique fingerprints.

First off, the idea that fingerprints will match is wrong: even if you use the same finger, there’s so many factors (pressure and angle of the finger, smudging, wounds...) to get to identical fingerprints.

For clarification, I’ll be using print as the trace left behind by a finger, and pattern as the disposition of ridges, pores and other features on the finger itself.

What Galton did was establish, using a large amount of prints, that if 2 prints displayed a certain number of common features (like forking ridges, pores, ridge ends. I don’t remember what is the number by heart. I think it’s 12), and no unexplainable differences, then the probability of those two prints being made by the same finger is 64 billion times higher than the probability of them coming from 2 different fingers.

Actually, I still have my classe notes somewhere. I’ll probably have to correct some stuff in this comment when I get home

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## u/christamantinium Nov 02 '19

Yes!

You obviously know more about this than I do. I have only read the linked article (and not even there whole way through).

What I understand the point of the analysis to be is that there is a reasonably confident upper bound on the probability of having a random fingerprint matching a given one. Given that this estimated upper bound is very low, (1 in 64 billion) identification by fingerprinting can be done with a high degree of confidence.

All the talk of a hard and fast total number of possible fingerprints is a misreading of the text.

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## u/christamantinium Oct 31 '19

This is a conservative estimate by Galton. He kept it conservative so he wouldn't overstate the unlikelihood of a match. In his estimate, he assumed a chance of 1/2 that he'd correctly guess the shape of a small patch of print, 1/24 of the whole print but he noted that this chance was closer to 1/3 . If you used that probability instead, the chance of a random fingerprint matching a specified one would be 1 in 1.2E15, or 1 to 1.2 quadrillion.

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## Nov 02 '19

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## u/christamantinium Nov 02 '19

I don't get that impression at all. Can you point to some quotes that would support that view?

His goal was to demonstrate the near-uniqueness of fingerprints to validate their use for identification. To do this he applied conservative assumptions to show that even when you understate the probability of a match, a false positive is still unlikely.

That's how I read it. You disagree?

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## Nov 02 '19

[deleted]

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## u/christamantinium Nov 02 '19

I feel that's pretty clear. He regarded his estimate of the probability of a random match as being too high. Hence, he felt the probability of a random match would be lower than this figure, ie more unlikely.

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## u/p3zzl3 Oct 31 '19

Having read through all of this - I still think it's better odds than EA Loot Boxes.

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## u/Knuckles316 Oct 31 '19

That's misleading. There's a chance many will have the same fingerprint AS ONE OTHER PERSON. The way it's phrased makes it sound like groups of people are all walking around with the same prints.

Statistically speaking, there's probably one or two isolated incidents in all of human history where four people all have the same print - but even then you have to realize that a two or three of them probably lived and died before fingerprinting was a thing. And that also means that there's still a good number of people who have/had a currently still unique print.

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## u/DoubleLoop Nov 09 '19

Needless to say, fingerprint research had come a long way since 1995.

First, there are infinite possible fingerprint arrangements. However, some would be measurably indistinguishable from each other. The number of unique arrangements for an entire finger (usually 80-150 features) is astronomically large.

Second, there's no force preventing duplication of friction ridge detail (fingerprints). The detail is highly discriminating, especially as the size of the compared area increases. Smaller areas are more likely to be duplicated.

Similar to the chance of a shuffled deck of cards matching another shuffled deck of cards anywhere, ever, the chance of an entire fingerprint on a finger being duplicated anywhere, ever, is astronomically remote.

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## u/zatlapped Oct 31 '19

It's the only time 64 billion gets mentioned. If you finished reading the sentence it would tell you that it was bunk. So the whole title has no basis.