Guilty or Not Guilty?

There is a murder. Vital DNA evidence is found at the scene. It is 100% certain that the DNA belongs to the murderer. The chance of anyone matching the DNA is 1 in a million.

The police find a match on their DNA database.

You are on the jury. Is the man Guilty or Not Guilty?

What is the probability he is innocent?

Originally posted by wolfgang59
There is a murder. Vital DNA evidence is found at the scene. It is 100% certain that the DNA belongs to the murderer. The chance of anyone matching the DNA is 1 in a million.

The police find a match on their DNA database.

You are on the jury. Is the man Guilty or Not Guilty?

What is the probability he is innocent?

If the police's database contains DNA of many millions of people then the probability he's guilty is low. Exact probability cannot be computed without more data.

Originally posted by wolfgang59
There is a murder. Vital DNA evidence is found at the scene. It is 100% certain that the DNA belongs to the murderer. The chance of anyone matching the DNA is 1 in a million.

The police find a match on their DNA database.

You are on the jury. Is the man Guilty or Not Guilty?

What is the probability he is innocent?

I'm assuming you mean there is 1 chance in a million that any particular person matches the DNA sample. In that case there would be about 6000 people who do match. In the absence of any other information it's 1/6000 chance that the police suspect is guilty.

Originally posted by luskin
I'm assuming you mean there is 1 chance in a million that any particular person matches the DNA sample. In that case there would be about 6000 people who do match. In the absence of any other information it's 1/6000 chance that the police suspect is guilty.

but what about the probability that any of those other 5999 people live within proximity of the murder?

Originally posted by wolfgang59
You are on the jury. Is the man Guilty or Not Guilty?
What is the probability he is innocent?

How would we know?
Where are the other evidence?

I think there is a reasonable doubt here...

This DNA evidence in conjunction with other potential evidence could be sufficient to remove all reasonable doubt, but it would depend on the nature of the other evidence, such as movements, motives, other circumstantial evidence, etc.

If the man is otherwise not known to be connected to the case, then perhaps this evidence alone is not enough.

I would be interested in knowing how this "1 in a million" chance was determined, because depending on the precision (and accuracy) of this number, it could either be very meaningful, or simply a figure of speech.

But given that the DNA evidence has a definite bearing on the case, and is much more verifiably accurate than any hearsay, it would be admissible in my court.

Originally posted by wolfgang59
There is a murder. Vital DNA evidence is found at the scene. It is 100% certain that the DNA belongs to the murderer. The chance of anyone matching the DNA is 1 in a million.

The police find a match on their DNA database.

You are on the jury. Is the man Guilty or Not Guilty?

What is the probability he is innocent?

It depends on other factors. All I know is his blood was at the scene for some reason - or that of someone like him (there are more than a million people on the planet; several thousand people would match this blood).

Originally posted by wolfgang59
There is a murder. Vital DNA evidence is found at the scene. It is 100% certain that the DNA belongs to the murderer. The chance of anyone matching the DNA is 1 in a million.

The police find a match on their DNA database.

You are on the jury. Is the man Guilty or Not Guilty?

What is the probability he is innocent?

Was there alcohol involved? There's always alcohol involved.

What? The two sentences "It is 100% certain that the DNA belongs to the murderer." and "The chance of anyone matching the DNA is 1 in a million." are inconsistent.

Originally posted by paultopia
What? The two sentences "It is 100% certain that the DNA belongs to the murderer." and "The chance of anyone matching the DNA is 1 in a million." are inconsistent.

They are two different statements that are entire consistent with each other.

The first indicates that the DNA was discovered in such a manner as it is certain that the person supplying the DNA is the same person who perpetuated the crime.

The second indicates the possibility that other people might also be able to supply DNA which is indistinguishable from the DNA found in connection to the crime, 1 out of every 1,000,000 can't be distinguished.

Think of it like this.

Suppose a bit of blue sweater was found at the site of the crime. The suspect was wearing a blue sweater at the time. There might have been other people also wearing blue sweaters as well, however.

It is the same with the DNA, only the chances of a match are not as great.

I think the DNA is planted there by the real killer. To blame someone else. I would!

Or perhaps it's planted there by the police because they *think* they know who is the killer. I've seen "The Practice".

Originally posted by forkedknight
but what about the probability that any of those other 5999 people live within proximity of the murder?

Depends. Did the murder take place in New York, the most populous city in the USA, or in Kleine Buiten-Achternevendam, NL, pop. 14½?

Richard

Originally posted by Shallow Blue
Kleine Buiten-Achternevendam, NL, pop. 14½?

14½ persons? Didn't the murder succeed to 100%? Did he survive barely?

Originally posted by wolfgang59
There is a murder. Vital DNA evidence is found at the scene. It is 100% certain that the DNA belongs to the murderer. The chance of anyone matching the DNA is 1 in a million.

The police find a match on their DNA database.

You are on the jury. Is the man Guilty or Not Guilty?

What is the probability he is innocent?

He did it but is not guilty because he worked in an abattoir ???

Originally posted by wolfgang59
There is a murder. Vital DNA evidence is found at the scene. It is 100% certain that the DNA belongs to the murderer. The chance of anyone matching the DNA is 1 in a million.

The police find a match on their DNA database.

You are on the jury. Is the man Guilty or Not Guilty?

What is the probability he is innocent?

I thought someone would tie this question back to the RHP cheating discussion by now. What criteria/probability do you use to establish "guilt beyond a reasonable doubt"?

Of course, the analogy between DNA matches and Fritz matches isn't exactly precise.