# Chances of two people having the same DNA?

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1. Nov 9, 2013

### Superposed_Cat

There are only a finite number of combinations of DNA that one can have while still being human so my question is what are the chances of two people having the same DNA?

2. Nov 9, 2013

3. Nov 9, 2013

### Enigman

But dna fingerprintting is done only at a few loci (edit-13 it seems for CODIS http://en.wikipedia.org/wiki/DNA_profiling )

Just for fun-
Going solely by wiki searches and high school math-
Assumption-1) individuals are unrelated.
2) All neucleotides are equally likely for a particular position. (don't know if that's valid...screws up the gene pool big time...)
3x10^9 base pairs
99.9% of these are same
3x10^8 base pairs
There are 3 nucleotides GTA
Ways of arranging three nucleotides in 3x10^8 long sequence=
3x10^8!/g!t!a!
Where g+t+a=3x10^8
The equation has $\binom {3*10^8 +2}{2}$ integer solutions.
4.5*10^16
Let a solution be $(g_i , t_i , a_i)$
So-
${\sum^{4.5*10^{16}}_{i}} ( 3x10^8!/g_i!t_i!a_i!)$

Don't know if it can be simplified through math further...but probability should be somewhere around 1 by more than 1 billion*...(too lazy to code Mathematica...don't know if its even possible...anyway computer's freaking slow...would take ages to cough up an answer for a calculation of this scale)

EDIT: mmm...interesting article...
http://articles.latimes.com/2008/jul/20/local/me-dna20
-slightly biased arguments but seems worth scrutiny...

Last edited: Nov 9, 2013
4. Nov 9, 2013

### UltrafastPED

Which is what it said in the references provided above ... though if the 13 loci are treated as independent, larger values are obtained. The Wikipedia article provides details as to why these larger numbers are not reliable.

I am white, mostly of northern and western European descent, but with some Lakota blood; I also have black and oriental relatives of various shades ... just because two people look different does not mean that they are not related!

Besides, identity requires 13 matches, not 9. So this article appears to be a defense lawyer type attack on the general validity of DNA profiling. The actual weaknesses are in the areas of contamination (see Wikipedia article again), and circumstances. There are many reasons why DNA may be present ... good police work will provide more evidence such as means, motive, and opportunity - without these any case is weak.

The long history of fingerprint identification has similar issues: how did the fingerprint get there? If it appears on a cartridge shell found at the scene of the crime the next question should be: is this the home of the person who owns the gun which fired it? Is this the weapon involved in the crime? Was the incident a crime? Thus the fingerprint alone, nor the associated DNA are insufficient evidence.

5. Nov 9, 2013

### Superposed_Cat

Are fingerprints enough?

6. Nov 9, 2013

### UltrafastPED

Enough for what? Having known several sets of identical twins, I would say that neither DNA or fingerprints would have been enough for them. Having known them fairly well, I could also conclude that if one was involved, so was they other ... so in that case either _might_ be enough, but the circumstances also need to be considered: method, motive, opportunity.

Read any Sherlock Holmes story ...

7. Nov 9, 2013

8. Nov 9, 2013

### Ygggdrasil

By sequencing the DNA from various individuals, scientists have found 15 million single nucleotide polymorphisms, 1 million short insertions and deletions, and 20,000 structural variants (The 1000 Genomes Project Consortium). Assuming each of these sites of variation has only two alleles and that none are synthetically lethal, this puts an estimate of the possible combinations from randomly assorting these variants at 2^(1.6x10^6) or 10^480000.

9. Nov 9, 2013

### Enigman

Actually many cases are such that where only a partial match is possible due to degradation.
And that's acceptable in court http://en.wikipedia.org/wiki/DNA_pr...vidence_of_partial_or_incomplete_DNA_profiles
Actually fingerprints are different for identical twins (http://en.wikipedia.org/wiki/Twin#Genetic_and_epigenetic_similarity) and DNA might be different too (http://www.scientificamerican.com/article.cfm?id=identical-twins-genes-are-not-identical)
Er...sorry ? How does a character witness implicate one twin with the other?
Read only Doyle's; others are pure rubbish...Eg. http://www.youngsherlock.com/
:tongue:
A case illustrating the opposite: conviction based only on DNA evidence presented (fallaciously according to http://plus.maths.org/content/os/issue55/features/dnacourt/index but I don't think the 'correct' interpretation would have affected much.) and all other evidence supporting innocence: