As with a lot of "simple" math, the trick is to actually write it down and calculate it, because our intuition (at least for some of us) is often not the best when it comes to this kind of calculation.
In this case we write down the contingency table. Assuming that the test perfectly detects what we are looking for we find
True positives: 1
False positive: 5% of 1000 = 50
True negative: 949
False negative: 0
Chance of disease given positive results = 1/51 = 1.96%
In this case we write down the contingency table. Assuming that the test perfectly detects what we are looking for we find
True positives: 1
False positive: 5% of 1000 = 50
True negative: 949
False negative: 0
Chance of disease given positive results = 1/51 = 1.96%