A particular city is serviced by three airlines for its passenger traffic. Airline A carries 50% of the passengers, Airline B 30%, and Airline C the remaining 20%. Each of the airlines is responsible for handling its security. The probabilities that a passenger carrying some type of weapon will be detected by Airlines A, B, and C are 0.9, 0.5, and 0.4, respectively.
If a weapon is detected on a passenger, what is the probability that Airline B detected it?