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A diagnostic test for the detection of COVID-19 gives a positive result 3% of the time for people who do not have the disease. The

A diagnostic test for the detection of COVID-19 gives a positive result 3% of the time for people who do not have the disease. The test gives a negative result 0.4% of the time for people who do have the disease. Suppose a large-scale investigation has shown about 6% of the population has COVID-19.

  1. Find the probability that a person selected at random would test positive for the disease.

  1. Given that a randomly selected person tests positive for the disease, what is the probability that the person does not have the disease?

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