At one automated international airport arrival location, facial identification software compares a camera image of the traveler with a scan of their passport picture. The procedure correctly concludes a match with 99.4% of males and 98.8% of females. The other cases have to be handled by agents.
(a) If half of the travelers are males, find the probability that the software will call a miss-match for a traveler with a correct passport.
(b) If half of the travelers are males and a miss-match occurs for a traveler with a correct passport, find the probability that the traveler is a male.