Question

You are a State Trooper on a roadblock. Since it is New Year’s Eve, you know from prior experience that approximately 5% of the drivers on the road have blood alcohol content over the legal limit of 0.08%. Your portable breathalyzer gives a PASS / FAIL reading. From prior experience and manufacturer’s data, you know that the breathalyzer has a “hit rate” of 90% and a “false positive rate” of 20%. That means that if the breathalyzer says FAIL, there is a 90% chance of it being correct if the subject is legally DUI and a 20% chance of a FAIL reading even if the subject is not legally intoxicated. You stop a driver at random and test him. He passes, so you let him go. What is the probability that the driver was legally DUI?

Answer 1

Something sounds weird. 90% + 20% = 110%

Answer 2

I do not agree that the false positive rate (on non-DUI) and the correct positive rate (on true DUI)have to add up to 100%

He could either be truly DUI and not caught or non-DUI and correctly passed. They are asking about the first possibility.

You know (because it says so) that 5% or the people driving are DUI at that time.

The probability that he was DUI and passed anyway was 0.05*0.1 = 0.005