With the recent threats of terrorism, airports are concerned about weapons detection at boarding gates. The detection rates for weapons carried on the person or in their carry-on luggage must be extremely high. In a particular city, airport A handles 50% of all airline traffic, while airports B and C handle 30% and 20%, respectively. The detection rates at the three airports are 0.99, 0.95, and 0.8, respectively.
a. What is the probability that a passenger found to be carrying a weapon through the boarding gate is using airport A?
b. What is the probability that a passenger carrying a weapon through the boarding gate is not detected?