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Probability of an event basedon given variables.

  1. Apr 17, 2013 #1
    For some time now I've been trying to figure out probably for a problem of the following form.

    Say a criminal profiler is trying to determine the probability that someone is a criminal based on statistical information.

    60% of people who have mustaches are criminals.
    70% of people who wear black hats are criminals.
    80% of people who wear sunglasses are criminals.

    If the profiler is profiling an individual who wears sunglasses, a black hat, and has a mustache; how would she determine the probability that this individual is a criminal?

    By the way, this is not a homework problem, I'm just trying to understand how to apply probability better.
    Thanks a lot.
     
  2. jcsd
  3. Apr 18, 2013 #2
    The events may or may not be independent. If they aren't independent, then there is no answer other than collecting data and measuring it directly.
     
  4. Apr 18, 2013 #3
    Could one at least establish an upper or lower probability limit? Would the individual in the example have at least a 80% probability of being a criminal based on the criteria that 80% of people who wear sunglasses are criminals? On the other would the probability of the individual being a criminal be at least 60% based on the "fact" that 60% of people with mustaches are criminals?
     
  5. Apr 18, 2013 #4

    mathman

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    Gold Member

    80% would be lower limit.
    If the criteria are independent, then the probability of being a criminal is
    1 - prob(at least one does not hold) = 1 - .4x.3x.2 = 97.6%.
     
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