Answer
The confusion of the inverse reflects the fact that the statement and its inverse are not the same thing.
Work Step by Step
We first consider the probability that a subject is infected giving a positive test result.
We use the equation for probability to find:
$P=\frac{number\ of\ desired\ outcomes}{total\ number\ of\ outcomes}$
$P = \frac{17}{17+2}=.895$
We now find the inverse, which is the probability that there is a positive test result given that the subject is infected:
$P=\frac{number\ of\ desired\ outcomes}{total\ number\ of\ outcomes}$
$P = \frac{17}{17+6}=.739$
Here, we see that the statement and the inverse are not equal, reflecting the confusion of the inverse.
