Imagine that human papillomavirus has a 40% incidence among people 21-30 years of age. A test for the virus has a 50% false negative rate but no false positive rate. If you get a negative test for the virus, what's the chance that you are infected?

The chance that I'm infected is 50%.

Explanation:

As with any screening test, an HPV test carries the risk of false-positive or false-negative results.

False-positive. A false-positive test result indicates that you have a high-risk type of HPV when you really don't. A false-positive result could lead to an unnecessary follow-up procedure, such as colposcopy or biopsy, and undue anxiety over the test results.

False-negative. A false-negative test result means you really do have an HPV infection, but the test indicates that you don't. This might cause a delay in appropriate follow-up tests or procedures

From the question, there's 40% incidence rate among people of age 21 - 30 years. And the test as a 50% false negative rate. Due to the high false negative rate, if I go for the test, the chances of false negative is 0.5 (50%).

50%

Explanation:

It simple. If the over-all false negative rate is 50% then the reason why there is 50% chance of me effected from papilloma virus is that my test result will have a 50% probability to be a false negative. Furthermore, it also depends on other factors like my age ...