1. Standard memberPBE6
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    31 Jul '08 14:25
    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?
    Food for thought:

    http://en.wikipedia.org/wiki/Prosecutor%27s_fallacy
  2. Joined
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    31 Jul '08 21:54
    Originally posted by PBE6
    Food for thought:

    http://en.wikipedia.org/wiki/Prosecutor%27s_fallacy
    Excellent 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...

    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.
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    31 Jul '08 21:56
    Originally posted by FabianFnas
    How would we know?
    Where are the other evidence?

    I think there is a reasonable doubt here...
    Then I was pretty right here!
    (I should be a legal advisor here, making big bucks!)
  4. Standard memberwolfgang59
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    01 Aug '08 07:52
    Originally posted by PBE6
    Food for thought:

    http://en.wikipedia.org/wiki/Prosecutor%27s_fallacy
    Yes 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!

    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 08:45
    Originally posted by FabianFnas
    14½ persons? Didn't the murder succeed to 100%? Did he survive barely?
    Well... 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.

    Richard
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    03 Aug '08 03:38
    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.
    Welcome back, Paul!
  7. Standard memberAThousandYoung
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    03 Aug '08 03:39
    Originally posted by FabianFnas
    14½ persons? Didn't the murder succeed to 100%? Did he survive barely?
    One of them is a midget.
  8. Standard memberAThousandYoung
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    09 Aug '08 21:15
    Originally posted by FabianFnas
    14½ persons? Didn't the murder succeed to 100%? Did he survive barely?
    Lost an arm, a leg, an eye and 16 teeth.

    And a testicle.
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    01 Sep '08 00:42
    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.
  10. Standard memberAThousandYoung
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    01 Sep '08 05:17
    Originally posted by UserChevy
    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.
    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.
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    01 Sep '08 07:00
    Originally posted by AThousandYoung
    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.
    And 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.

    Richard
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    01 Sep '08 15:48
    Originally posted by AThousandYoung
    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.
    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?
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    01 Sep '08 22:00
    Originally posted by UserChevy
    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?
    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.
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    02 Sep '08 01:32
    Originally posted by geepamoogle
    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.
    Very 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.
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