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13 September, 01:06

A certain disease has an incidence rate of 0.4%. If the false negative rate is 7% and the false positive rate is 5%, compute the probability that a person who tests positive actually has the disease.

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  1. 13 September, 03:46
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    The incidence rate is = 0.4% or 0.004

    The false negative rate is = 7% or 0.007

    The false positive rate is = 5% or 0.005

    The probability is

    0.05 * (1-0.004) + 0.95*0.004

    = 0.0498 + 0.0038 = 0.0536

    Probability that a person who tests positive actually has the disease would be represented as:

    Let the probability be represented by = p

    p * 0.0536 = 0.95 * 0.004

    p = 0.0038/0.0536

    p = 0.0708

    Hence, probability is 0.0708
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