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Probability question

  1. Nov 23, 2003 #1
    Hi all,

    I think this would be a probability question.

    We do a random check. 10% smokes marihuana. This test gives the right results in only 90%. One person is tested positive. How big is the chance that he really smoked marihuana?
    -if there are 8 people in total.
    -is it also possible to make an assumption if the size of the group is not known?

    thanks a lot!

    Martine
     
  2. jcsd
  3. Nov 23, 2003 #2
  4. Nov 25, 2003 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Since everything is given in terms of percentages, the actual total number is irrelevant.


    Suppose there were 100 people tested. Assume that 10% of them (10) actually smoke marijuana, 90 do not.

    The test is 90% accurate (I assume that is both 10% false positives and 10% false negatives- often those are two different numbers).

    Of the 10 people who actually do smoke, 9 will test positive and 1 negative.

    Of the 90 people who do not, 81 will test negative and 9 positive so that we have a total of 18 positives and 82 negatives.

    Given that a person tested positive, he/she is in that group of 18 positives. Of those, actually only 9 were actuall pot smokers so the probability that a person actually smokes marijuana, given that he/she tested positive, is 50%.
     
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