1. How strong is DNA evidence?
DNA matching
How strong is DNA evidence?

2. How strong is this evidence?
It’s a match!
The data:
An evidence sample from the crime scene is compared with a reference sample taken from the suspect.
DNA profiles are unique to each individual person (other than identical twins, triplets, …)
The whole DNA profile is not matched, but only around 13 points.
But matching 13 particular points of comparison, say, means that the probability of a match by chance is very small – less than the probability that you choose all 6 lottery numbers this week!
A sample of DNA from a crime scene ‘matches’ a sample from the suspect.
How strong is this evidence?

3. How strong is this evidence?
It’s a match!
In fact, the probability that two samples of DNA match by chance may be as small as 1 in a billion.
So surely, this must be absolutely certain evidence that the person is guilty?
Well, with other evidence, it may be, but there are several arguments which should be considered before a decision is made.
A sample of DNA from a crime scene ‘matches’ a sample from the suspect.
How strong is this evidence?

4. Prosecutor’s fallacy
The correct argument:
The chance is 1 in a million that some other particular person left the evidence at the crime scene.
This is NOT the same as the chance that someone (anyone) else left that evidence.
If the population size with access to the crime scene is 1 million, then a chance match is perfectly possible.
If the chance of a match is 1 in a million, that means the probability that someone else is guilty is 1 in a million.

5. Defence lawyer’s fallacy
This would only be correct if all these other people had the same access to the crime scene.
Since there thousands of people who might be a match for this DNA, the chance that this particular person is guilty is only 1 in several thousands.

6. Dependence and independence
Challenging the maths
The calculation of the probability 1 in a billion uses the product rule for independent events.
It does not apply when events are not independent.
So if the local population is mixed or inbred, so that the distribution of DNA is not typical of the population generally, then the strength of the DNA evidence may be over-stated.
Dependence and independence

7. It was my brother who did it!
If the suspect is not the guilty party, then the similarity between the DNA samples needs to be explained.
A relative may be the guilty person.
Close relatives have very similar DNA.

8. There is always a small probability of a false positive test.
This does not mean that two people might have the same DNA, but it does mean that there can be error in the test process.
There is also a small chance of error in the tests because of the way that the evidence was collected, or how the test was conducted, or how the test results were reported.