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Do you convict?

  1. Mar 10, 2012 #1


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    Rather than a made up brain teaser, a real court case from 1964: http://www.law.berkeley.edu/faculty/sklansky/evidence/evidence/cases/Cases%20for%20TOA/People%20v.%20Collins.htm [Broken] (Spoiler alert: The court record provides an answer to this 'brainteaser', but their answer may or may not be correct - they are judges trained in the legal profession, after all.)

    If the characteristic individual probability of each item testified to is:

    A. Partly yellow automobile 1/10

    B. Man with mustache 1/4

    C. Girl with ponytail 1/10

    D. Girl with blond hair 1/3

    E. Negro man with beard 1/10

    F. Interracial couple in car 1/1000

    Never mind the fact that the probabilities were entirely made up by the prosecution with the disclaimer that the jury was free to substitute whatever they felt the probability of each attribute was. If the probabilities listed were accurate, what's the probability that the defendants are innocent? Based on that probability, do you convict them?
    Last edited by a moderator: May 5, 2017
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  3. Apr 6, 2012 #2


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    Sounds interesting. I'm almost certain my simple analysis is missing some critical piece of intelligent thought, rendering it essentially useless.

    Some of these probabilities are not mutually independent. For instance, I imagine the probability of sporting a mustache is significantly higher than 1/4 among men with beards. In any case, let's say the probability, p, is about 1 in 10^6 that a randomly chosen couple have all of the specified attributes. The question then is: what is the probability that there exists at least one other couple matching this description that can be found within an appropriately selected population sample, given that there already exists one such couple. If the sample size is N, this probability is: p'(N)=1-((1-p)^N). If p=1/10^6, then (approximately):
    P'(N)=10^(log(N)-6) for N<10^5, and for instance, P'(10^6)=37%

    To estimate likelihood of innocence, I'd have to know a few things about the population density in the San Pedro area in 1964, and confirm that mid-day of June 18th that year was not special in any way (no big sporting event, parade, etc. that would attract large numbers of people). And an area would have to be selected based on locations of events and the size of the error bars in time estimates of the witnesses.

    I haven't given much thought to what I consider "beyond a reasonable doubt" (I haven't served on a jury). My level of reasonable doubt, I think, depends on some kind of ratio of the seriousness of the consequences were I wrong, to the benefit of the action were I right. For instance (to make a rock climbing/mountaineering analogy), my decision to climb a mountain via some particular route is dependent on the estimated awesomeness of the climb and the likely seriousness of injury from a fall. For a really awesome climb where I'm only likely to break bones, I'd do it if I'm even just 90% sure of success. For a not-so-awesome climb with the potential for a death fall, I'd probably want to feel about 99.99% sure of surviving. Translating injury to jail time for a robbery conviction and the feeling of accomplishment of climbing a mountain with the feeling of accomplishment from advancing justice and the protection of individuals from purse snatchers, I'd have to say that my doubt would have to be smaller than 1/10, closer to 1/100. I wouldn't convict if I arrived at a P' > 1/10, and would almost certainly convict with P' <1/100.
    Last edited: Apr 6, 2012
  4. Apr 7, 2012 #3


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    The prosecution's calculations were that there was a 1 in 12 million chance that the suspects were innocent, but that's not actually what he calculated. In fact, if I were the defense lawyer, I would have said the prosecution calculated that there was a 1 in 12 million chance that my client (the defendants) were an interracial couple consisting of a man with a beard and mustache and a blonde woman that owned a yellow car - a calculation that's meaningless since everyone in the court room can simply look at the defendants and at least know their race.

    Just leaving the fact that the numbers were entirely made up, the calculations of the prosecutor were actually a way to calculate the average number of people meeting that description that were likely to exist in Los Angeles at some given time. That's not even the probability of there being a less than average number of people meeting that description or a higher than average number of people meeting that description; let alone that this particular couple meeting that description were the guilty party.

    It's a little like the classic problem:

    A disease exists that's virtually always fatal and it strikes 1 out of every 1000 people. Fortunately, a test exists to find out if you're suffering from this disease and the test is 99% accurate. Unfortunately, you test positive for this disease. Fortunately, a company is marketing a new miracle cure* that results in 90% of the people testing positive for the disease surviving with absolutely no side effects (and the success rate is legitimate and verifiable). Unfortunately, the cure costs $40 an ounce with the suggested dosage being one ounce per day. Is the cost of the cure worth it to you?

    miracle cure*: The active indredient of the cure consists of monohydroden dioxide, which is known to have very few negative side effects, provided it's used as directed.
  5. Apr 25, 2012 #4
    Both the questions and the answers given make no sense. All that probability stuff is meaningless dribble.

    My answer is I do not convict. Can't be in two places at same time. The female defendant could not be both at the employers home and robbing this lady in an ally at 11:30am. Then, the employer could not see the male defendant pick up the female defendant in a yellow car if the female defendant had to run down some ally to enter a yellow car at the end of that ally without also seeing the crime being committed. Then there is the matter of the lighter hair color that needs to be accounted for. Question? How far from the seen of the crime does the employer live? Was there enough time for the female defendant to get off work, drive to where the victim was, see her, determine that she had something of value, get out of the car from behind the victim, run or walk a short enough distance as to not make enough noise for the victim to notice her coming, run out of the ally to a car (the witness did not say he saw drive up) waiting for her. The witness says he was watering his yard so he would have noticed the car drive up. If he did not, that would mean the car was there long enough for the female to be placed in the ally and lay in wait or walk/run from the employers house to commit the crime and enter the car. So, how long was the witness watering his grass?

    For me there is too much happening in too short a period of time.
  6. Apr 25, 2012 #5


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    I was way off the mark. My first thought was:
    "Hey, that nice young lady is taking off after the robber!"
    My second thought was:
    "Hey, that nice young lady jumped in a yellow cab to chase down the robber!"
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