An air traffi c controller at Dulles Airport must obey regulations that require her to divert one of two airplanes if the probability of the aircraft’s colliding exceeds 0.025. The controller has two inbound aircraft scheduled to arrive 10 minutes apart on the same runway. She knows that Flight 100, scheduled to arrive fi rst, has a history of being on time, 5 minutes late, and 10 minutes late 95, 3, and 2 percent of the time, respectively. Further, she knows that Flight 200, scheduled to arrive second, has a history of being on time, 5 minutes early, and 10 minutes early 97, 2, and 1 percent of the time, respectively. The fl ights’ timings are independent of each other. (a) Must the controller divert one of the planes, based on this information? (b) If she fi nds out that Flight 100 defi nitely will be 5 minutes late, must the controller divert one of the airplanes? (c) If the controller fi nds out that Flight 200 defi nitely will be 5 minutes early, must she divert one of the airplanes?
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