31 Jul 08
Originally posted by wolfgang59Food for thought:
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?
http://en.wikipedia.org/wiki/Prosecutor%27s_fallacy
31 Jul 08
Originally posted by PBE6Excellent link. It provides an answer in the matter that is clearer than the manner in which I put it, but for those who did not check it out, here is what I took from it...
Food for thought:
http://en.wikipedia.org/wiki/Prosecutor%27s_fallacy
The usefulness of such testing and the probability of random matches would depend very much on the size of the samples looked through and the odds of the person's guilt without the DNA evidence.
In the event the suspect had other significant evidence against him, the DNA evidence would remove almost all reasonable doubt.
However, if the suspect was randomly found amongst a very large sample, and the prosecutor did not have much else in the way of other evidence, then the DNA evidence would probably be next to useless for the moment, because there would still be reasonable doubt of the person's guilt.
So the question of his chance of guilt does not have a definitive answer, because any definitive answer would be heavily influenced by context we are not given, and thus we cannot give a meaningful numerical value to it.
01 Aug 08
Originally posted by PBE6Yes excellent link! The problem is of course all about CONDITIONAL PROBABILITY. Quite easy to grasp when you think about it but I think we all have the initial knee-jerk reaction that the guy is guilty!
Food for thought:
http://en.wikipedia.org/wiki/Prosecutor%27s_fallacy
I got this problem from an excellent book I picked up at the Charity Shop called "A Mathematician Reads The News". I will supply author later when I remember.
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01 Aug 08
Originally posted by FabianFnasWell... in Dutch, we have a saying for a place (town, building) that either is nearly abandoned or has a tiny population: we say it contains "one-and-a-half man and a horse's head". Apparently this fictional backwater village of mine is slightly less abandoned than that, but not by much.
14½ persons? Didn't the murder succeed to 100%? Did he survive barely?
Richard
01 Sep 08
Originally posted by UserChevyThat assumes all 6683 people are near by and likely to leave a sample on the scene. More likely they're scattered all over the globe and only one is anywhere close by.
1 in a million match the DNA, so out of 6.684 billion people in the world, 6684 people match the DNA, so only 1 obviously is the murderer, so 6683 people with the correct DNA are innocent, so the probablity that the man is innocent is 6683/1.
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01 Sep 08
Originally posted by AThousandYoungAnd that assumes that DNA is spread evenly over the globe. It ain't so, even for the relatively useless markers they use for DNA profiling.
That assumes all 6683 people are near by and likely to leave a sample on the scene. More likely they're scattered all over the globe and only one is anywhere close by.
Richard
01 Sep 08
Originally posted by AThousandYoungThe riddle just said that they found someone with the correct DNA. It never said where they found that person. Maybe the killer fled accross the globe?
That assumes all 6683 people are near by and likely to leave a sample on the scene. More likely they're scattered all over the globe and only one is anywhere close by.
01 Sep 08
Originally posted by UserChevyWhich is why my answer is that context determines EVERYTHING!
The riddle just said that they found someone with the correct DNA. It never said where they found that person. Maybe the killer fled accross the globe?
A DNA match is enough to push a borderline case into a definite conviction, but not enough to stand on its own.
02 Sep 08
Originally posted by geepamoogleVery true. Bottom line, to answer the main question, if I was on the jury I would say not guilty provided just with the DNA evidence.
Which is why my answer is that context determines EVERYTHING!
A DNA match is enough to push a borderline case into a definite conviction, but not enough to stand on its own.