5. Air Travel. (10 points) Three different airlines, United, Southwest, and American y out of SFO. United airlines has 70 ights per day, of which 10% are late because of mechanical problems, Southwest airlines has 70 ights per day, of which 15% are late because of mechanical problems, and American has 140 ights per day, of which 5% are late because of mechanical problems. Weather can also cause planes to run late. The probability that a ight is late because of weather given that it was originally on time is 5%. If the plane is already late because of mechanical problems, then it will be late for sure regardless of the weather. Assume there are no other airlines that y out of SFO. (a) Draw a tree and the corresponding conditional probabilities for this random sa quential experiment. (b) What is the probability that a ight leaving SFO is late (either because of me chanical problems or weather)? (c) You randomly hear someone at the airport complaining about a late flight, but do not hear them say which airline. What is the probability that the airline is American