The U.S. Department of Transportation reported that during November, 83.4% of Southwest Airlines' flights, 75.1% of US Airways' flights, and 70.1% of JetBlue's flights arrived on time (USA Today, January 4, 2007). Assume that this on-time performance is applicable for flights arriving at concourse A of the Rochester International Airport, and that 40% of the arrivals at concourse Aare Southwest Airlines flights, 35% are US Airways flights, and 25% are JetBlue flights.
a. Develop a joint probability table with three rows (airlines) and two columns (on-time arrivals vs. late arrivals).
b. An announcement has just been made that Flight 1424 will be arriving at gate 20 in concourse A. What is the most likely airline for this arrival?
c. What is the probability that Flight 1424 will arrive on time?
d. Suppose that an announcement is made saying that Flight 1424 will be arriving late. What is the most likely airline for this arrival? What is the least likely airline?