In July 2005, the journal Annals of Internal Medicine published a report on the reliability of HIV testing. Results of a large s

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In July 2005, the journal Annals of Internal Medicine published a report on the reliability of HIV testing. Results of a large s

tudy suggested that among people with HIV, 99.7% of tests conducted were correctly positive, while for people without HIV, 98.5% of tests conducted were correctly negative. A clinic serving an at-risk population offers free HIV testing, believing that 15% of the patients may actually carry HIV. What's the probability that a patient testing negative is truly free of HIV?

Mathematics

1 answer:

pashok25 [27] · Answer 1 · 2024-01-21T16:52:36+03:00

The probability that a patient with a negative result is truly HIV-free is 0.999.

<h3>How to find the probability that the negative result is correct?</h3>

To find the probability that confirms that the result of the HIV test is negative, we must take into account the information provided in the information and perform the following mathematical operation.

The probability that No HIV and test positive is:

P = 0.85 * 0.985

P = 0.8372

The probability that HIV and test negative is:

P = 0.15 * 0.003

P = 0.00045

The probability that No HIV and negative test of HIV and negative test is:

P = 0.00045 + 0.8372

P = 0.8377

P = (NOT HIV / Test)

P = 0.8372 / 0.8377

P = 0.999