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22 September, 16:09

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The test to detect the presence of a liver disorder is 98% accurate for a person who has the disease and 97% accurate for a person who does not have the disease.

If 3.5% of the people in a given population actually have the disorder, the probability that a randomly chosen person gets an incorrect diagnosis is

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  1. 22 September, 16:16
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    The probability that a randomly chosen person gets an incorrect diagnosis is 2.965% = 0.02965.

    Step-by-step explanation:

    Given, The test to detect the presence of a liver disorder is 98% accurate for a person who has the disease.

    so, probability of incorrect diagnosis = 100-98 = 2% = 0.02.

    and 97% accurate for a person who does not have the disease.

    so, probability of incorrect diagnosis = 100-97 = 3% = 0.03.

    And 3.5% of the people in a given population actually have the disorder.

    ⇒ the probability that a randomly chosen person gets an incorrect diagnosis is (3.5% * 0.02) + (96.5% * 0.03) = 2.965% = 0.02965.
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