The Customs Inspection agency at international airports has developed a traveler profiling system (TPS) to detect passengers who are trying to bring more liquor into the country than is allowed by present regulations. Long-term studies indicate that 20% of the passengers are carrying more liquor than is allowed.
Tests on the new TPS scheme has shown that of those carrying illegal amounts of liquor, 80% will be identified and subject to complete luggage search. In addition 20% of those not carrying illegal amounts of liquor will also be identified by TPS and subject to a complete luggage search.
If a passenger is identified by TPS, what is the probability that the passenger is carrying an illegal amount of liquor? Comment on the value of this system.