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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

.

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.