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Canadian Border services at the Bluewater Bridge in Sarnia, Ontario 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 passengers are carrying more liquor than is allowed. Tests on the new TPS system has shown that of those carrying illegal amounts of liquor, 80% will be identified and subject to a complete vehicle search. In addition, 20% of those not carrying illegal amounts of liquor will also be identified and subjected to a complete vehicle search.
a. What is the probability that a traveler is carrying an illegal amount of liquor and is identified as a suspect?
b. What is the probability of a traveler being identified by the TPS system as a suspect?
c. If a traveler is identified, what is the probability that the traveler is carrying an illegal amount of liquor?
d. If a traveler is not identified as a risk, what is the probability that the traveler is carrying an illegal amount of liquor?
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