The person whose DNA was found at the scene is a “freebie” in the sense that he does not count against the other 9.

That’s why the odds of guilt are 1:9.

If you pick DNA at random, you would expect 9 matches total. If you pick a PERSON at random, you would expect 10 people with the same DNA, including the person you originally picked.

1) A murder case depends *entirely* on DNA evidence.
2) DNA from the perpetrator was found at the scene.
3) The probability of a match between the DNA found at the scene and any one person at random is 1.1 million to one.
4) Given the population of the state or area, we can expect nine people to match the DNA found at the scene, at random.
5) We do not know how the police came across the defendant, and we may not speculate about it.

If the DNA was definitely left by the perpetrator, and we have good reason to believe the perpetrator has not left the state or area, we know that one person in the state or area must have committed the murder.

We may assume that anyone who is not a match for the DNA left at the scene is actually innocent.

We are left with the genetic equivalent of an Agatha Christie mystery, where there are nine possible suspects, one of whom is definitely guilty.

In the absence of any other information, each suspect has one chance in nine of being the guilty party. If you put their pictures on a dartboard and throw a dart, you have one chance of hitting the perpetrator, and eight chances of hitting an innocent person.

So my vote is 8:1, in favor of innocence.

BONUS ROUND: Having given me your best shot at the answer, which of the above 13 do you think your fellow jurors are most likely to believe? If it’s a different answer from yours, why?

Having served on two juries, I believe my fellow jurors would believe it’s too hard to decide. Between 7 and 11 jurors would go with whoever sounds the most authoritative, and 1-4 with whatever supports their biases.

No. The hypothetical doesn’t say how he was chosen. He may have been caught at the scene. He may have been chosen because the cops took a DNA sample from the scene, put him into a database, and found a hit.

Right, but in both of your examples, a DNA profile was found at the scene, before you had looked at a single record in the database. That’s why he’s a gimme. Theoretically, a record from the database could have the same effect, if he was pulled early enough in the process, such that you have 1 known member of that DNA race, and still have essentially 18 million unknowns to go. Where it differs is if you had to dig through 1.1 million records to find that first sample.

Your example is based on the case of Mr. Puckett; You cannot say that Mr. Puckett “wasn’t chosen based on matching or not-matching any particular genetic makeup”!

Puckett (the record selected from the database because it generated a match) was chosen based on matching or not matching a particular make-up. The perp (the DNA found at the scene of the crime) was not. He’s the freebie.

I don’t think the pattern you describe holds true for all patterns that could match anybody. It does hold for all patterns known to match one person, who can then be matched up against a database full of unknowns. In other words, in a database of 10 million unknowns, and with an RMP of 1.1 million to 1, you should expect to find aproximately 9 matches, not 9 + 1. The +1 guy is the one you already knew about independently of the database (or didn’t).

How many Californians match a particular profile not konwn to match anybody? Based on todays’ population size, probably about 20. How many match yours? 21.

No. The hypothetical doesn’t say how he was chosen. He may have been caught at the scene. He may have been chosen because the cops took a DNA sample from the scene, put him into a database, and found a hit.

Your example is based on the case of Mr. Puckett; You cannot say that Mr. Puckett “wasn’t chosen based on matching or not-matching any particular genetic makeup”!

* * *

What you’re talking about–that the DNA at the scene must belong to somebody–is much less than what I describe above.

The +1 effect I describe does occur where you would expect on average 0 matches for each DNA pattern. (Such as if you have 6B people and 6 trillion possible DNA patterns)

But the effect I describe also holds true even where you expect about 9 matches on average for each DNA pattern (such as if you have 10M people, and a 1-in-1.1M chance of a match for any given random sequence). The effect I describe is not based on the fact that some patterns will be “empty”–in fact, it holds true even if every single pattern has at least 1 person.

Ok, that’s the quote of the day.

Otherwise, a full DNA match, with an RMP in the quadrillions, predicts that no one will have any particular DNA make-up. That’s usually an accurate prediction if you start with a hypothetical DNA sequence no living human is known to share, but it’s always off by one if you compare it to the real DNA sample. The odds of you having your own DNA may be a quadrillion to one, but I’ll bet you have it anyway.

If there are 11,000,000 people, with 1,100,000 unique, randomly-distributed DNA patterns, you might think on average there would be 10 people per unique DNA pattern. You would be right.

BUT if you count per PERSON, the average number of PEOPLE who share their DNA pattern, the average goes up to 11.

I don’t know why it’s always a boost of exactly +1, but I get the same answer whether I use very big or very small numbers.

* * *

Further, in the above example, approximately 8.3% of all people will have DNA patterns shared by more than 15 people. So in 8.3% of your cases, the odds are actually more like 15-to-1 in favor the DNA not being a true match. That’s a significant fraction of cases in which using the FBI’s base figures results in significantly underestimating the likelihood it’s not a true match.