Fingerprints are often used by law enforcement to identify individuals, even with a partial print. Are there any cases where people had the same fingerprints? Is there a limit to the number of unique fingerprints that can possibly exist?
@ChrisW Saw that question but it relates more to possible human errors and other factors when processing fingerprints, so I thought this deserved it's own question– msmucker0527Aug 28, 2014 at 18:07
In theory, no, but the odds for it happening are really low.
This presentation has a slide with an overview of the literature on the subject. If I'm interpreting the chart copied below, estimations of the possible configurations of fingerprints (i.e. the probability of a given fingerprint occurring) range from 1.45x10-11 to 1.20x10-80. Given that the number of people who have ever lived is estimated to be 100 billion to 115 billion (1.15x1011), then it's mathematically possible for every human who ever lived to have unique fingerprints.
Since there's nothing which hands out fingerprints and ensures uniqueness, it's quite possible that there have been duplicates at some point. However, the odds for duplicates actually coming up in a real world scenario (i.e. two people living in the same country within the same general span of time, instead of anywhere in the world at any point in history) are infinitesimal.
Added to address comments: It's worth noting that all these probabilities are based on the granularity of the method involved. The Galton method, for instance, seems to involve dividing the finger up into 24 regions, and identifying the most prominent feature of that region. This leads to a fairly granular set of results, which, in turn, means that it's much easier to find someone else who would register as having the same set of fingerprints. This would be roughly equivalent to a version of the birthday problem where you're trying to find people who have the same birth month, instead of the same birthday.
Modern matching systems use the minutia of the fingerprint to provide a much more accurate match. My understanding of it is that there are 36 points selected based on finding certain features in a general area (i.e. five points of interest in this small section), and the precise relative location of each point to each other is what makes up the modern fingerprint record. This produces a far more accurate digital record of the fingerprint, although still not a 100% perfect one. Correspondingly, this makes the chances of finding two fingerprints considered to be a match much lower. To extend the previous analogy, you're now trying to find two people who share a birth minute, not just a birth day.
1This begs the question of how similar two "different" fingerprints might be. Are we talking about differences you could see with the naked eye, or microscopic differences? Also as a point of interest, if Galton were right, then it only takes around 400K people to get a 50-50 shot of two people having the same fingerprint, meaning it would be very unlikely for there NOT to be two people in the US with identical fingerprints. Aug 28, 2014 at 22:56
1@RobWatts - The presentation I linked to goes into somewhat more detail, although it's obviously meant to accompany a talk. I did a bit more reading and basically, Galton's method isn't considered very accurate. The "minutiae" method uses each ridge split or join, which is more precise and what most use today (I think).– BobsonAug 29, 2014 at 14:03
@Bobson: You oversaw the problem of the birthday paradox. If we assume a fair distribution each fingerprint occupies randomly one slot. The birthday paradox approximately increases the probability squarely with the number of people involved (Halmos upper bound for p=50%: sqrt(2*N*ln(2)). If N = 10e11 then a duplicate is to expected with 370 000 people ! Given the number of people on earth we need at least a probability of 1/2.59e19 which is much more than expected. Galton will lead to a duplicate, Henry, Balthazar and Bose are possible.– user13486Aug 31, 2014 at 19:19
@ThorstenS. - Since you're the second person to mention that, I edited the answer to address it. Basically, Galton's method was the very first, and isn't in use today for precisely that reason.– BobsonSep 2, 2014 at 5:20
Is there any reason to believe that Stoney's 10^80 "possible fingerprints" are anywhere close to being equally probable? If two people were to each flip 1,000 coins, there would be 1,001 different values for the number of heads each person flips, but the probability of two both people flipping the same number of heads would be much greater than 1/1,000.– supercatSep 5, 2014 at 23:36