The answer should be 4E^-6

The current test for the H7N9 Avian flu is a blood test. It requires withdrawing blood from the person (painful) and taking that blood for assaying at an authorized laboratory (expensive). Thankfully, your professor created the aptly-named Duck test. On a selected sample of n=20 Americans, he clinically tested it. The following confusion matrix gives the results of that clinical testing.

Test Results

positve Dis:4 clean2

negative Dis1 clean13

This shows the new test has a false positive rate of 2/6 and a false negative rate of 1/14. While the first is poor, the second is pretty darned good!

Currently, the prevalence of H7N9 is rather low, just 1 in a million. Regardless, after returning from Beijing, your professor tested positive for H7N9 using the Duck test. So, given that he tested positive for the bird flu, what is the probability he actually has H7N9?