[pandaman]

I don't follow. The example in the wikipedia uses the opposite error rates to what you have given: it falsely flags a sober driver in 5% of cases. And it works because the stipulated rate of drunkenness is much lower than 5% (0.1%) so the false positives overwhelm the true positives. In your setup the positive detection should be accurate at 95%, the negative error (a drunk driver passed as sober) - would be around 0.005%, where did you get 1.96%?

Furthermore, as Wikipedia article noted, this assumes total testing. I highly doubt cops are walking around and drug test everyone they see.

[Atheros]

You're right! I wrote it backwards! I swapped the 95 and 100% in the post above.

My claim is that the cops in the article are walking around drug testing widely. Not literally everyone they see but if they are testing every white residue they see during any interaction with anyone, including bird droppings on the hood of someone's car, we've reached that point for all statistical purposes. The base rate fallacy will start applying.

[pandaman]

Base rate fallacy will start applying when the test's false positive rate is comparable to the frequency of the event. In the US cops usually don't show up at all when called, for cops to show up and do drug testing somebody needs to do something outrageous and the probability of the same person doing drugs is pretty high IMHO so the test with 4% error rate is going to be just fine. Of course, for the drugs conviction, the actual drugs need to be found but from what I understand, this article is about somebody arrested based on a drug test, then charged with a different crime and a sneaky lawyer, unable to fight the charges, trying to throw the case based on the "faulty test".