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23 March, 14:32

A certain disease has an incidence rate of 0.2%. If the false negative rate is 8% and the false positive rate is 4%, compute the probability that a person who tests positive actually has the disease.

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  1. 23 March, 17:23
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    32%

    Step-by-step explanation:

    Imagine 100000 people are tested.

    Of these 100000:

    10000080.02 = 2000 will have the disease

    8% of them:

    2000*0.08 = or 160, will test negative and the remaining 1840 will test positive.

    Of the 98000 who do not have the disease, 4% will test positive:

    98000*0.04 = 3920 will test positive

    So of the:

    1840+3920 = 5760 total people who test positive, 1840 will have the disease

    Thus, the probability is:

    1840/ 5760 ≈0.3194 = 32%

    So, out of people who test positive actually 32% has the disease.
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