Suppose on a given Monday night one out of every 1000 drivers on I64 is legally drunk (this is surely optimistic). The police have a field sobriety test which never fails to detect a truly drunk driver, but also falsely indicates drunkenness 5% of the time for sober drivers. Suppose a (uniformly) randomly chosen driver is stopped, the test is administered, and indicates drunkenness.

a. With what probability is the driver drunk? Show the calculation.

b. Compare your (correct, I'm sure) answer above with your conjecture about the typical response you may receive if you polled 100 random people with this question at your favorite bar or library one day. Briefly explain any predicted discrepancy.