A virus has been spread around a population. The prevalence of this virus is 84%. A diagnostic test, with a specificity of 94% and sensitivity of 15%, has been introduced. If a patient is drawn randomly from the population, what is the probability that: a) a person has the virus, given that they tested positive? b) a person has the virus, given that they tested negative?

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Liam Everett · Accepted Answer

First of all Let&#039;s define what Sensitivity and Specificity of a test are:- Sensitivity is defined as      P    [      T    +        |    D  ]- Specificity is defined as      P    [      T    −        |        D    ¯    ]Where       T    +    ,      T    −   indicate positive and negative test result while   D is &quot;disease&quot;Second let&#039;s take 10,000 persons and see what is happening with the given probabilities                          D        i        s        e        a        s        e                    N        o        t                 D        i        s        e        a        s        e                    T        o        t        a        l                            T        +                    1260                    96                    1356                            T        −                    7140                    1504                    8644                            T        o        t        a        l                    8400                    1600                    10000            What you are requested to calculate is(a)       P    [  D      |        T    +    ]  =      1260    1356    ≈  92.92  %and(b)       P    [  D      |        T    −    ]  =      7140    8644    ≈  82.60  %

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