4.77 Airport Security Suppose that, in a particular city, airport A handles 50% of all airline traffic, and airports B and C handle 30% and 20%, respectively. The detection rates for weapons at the three airports are 0.9, 0.5, and 0.4, respectively. If a passenger at one of the airports is found to be carrying a weapon through the boarding gate, what is the probability that the pas- senger is using airport A? Airport C?