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Math Help - Simple problem but need help from the experts

  1. #1
    Nimzovich
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    Simple problem but need help from the experts

    A test for a disease has a probability of 10% to give a false negative, this probability is not conditioned to anything else besides the test (is inherent to the test alone.).

    The posibility of the test to give false negatives when taken twice is 0.1 x 0.1 ? 1% is this correct? (meaning the probability that both are negative)

    take into account:

    The results of the test is independent from previous results.

    the question is not whether the person has the disease or not since that would most likely include conditional probability associated with epidimiology statistics (i.e. how many of the population have the disease) in which case Bayen would be used.

    thanks I appreciate your opinions.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Nimzovich View Post
    A test for a disease has a probability of 10% to give a false negative, this probability is not conditioned to anything else besides the test (is inherent to the test alone.).

    The posibility of the test to give false negatives when taken twice is 0.1 x 0.1 ? 1% is this correct? (meaning the probability that both are negative)

    take into account:

    The results of the test is independent from previous results.

    the question is not whether the person has the disease or not since that would most likely include conditional probability associated with epidimiology statistics (i.e. how many of the population have the disease) in which case Bayen would be used.

    thanks I appreciate your opinions.
    The probability of a false negative on a composite test that consists of two
    stages each with a probability of a false negative of 0.1 is indeed 0.01.

    This is independent of what is done after the first test if it is positive, as
    we are only considereing the results on subjects who do have the disease,
    and test negative.

    So we may think of it like this 100 diseased individuals come to the lab how
    many (on avaerage) do we send home reassured? Well 10 of them as clear
    on the first test, and of those 1 is clear on the secons and sent home
    reassured, thus 1% or 0.01 probability of false negative on the two stage test.

    RonL
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