The Bureau of Transportation Statistics reports on-time performance for airlines at major U.S. airports. JetBlue, United, and US Airways share terminal C at Boston’s Logan Air-port. The percentages of on-time flights reported for August 2012 were 76.8% for JetBlue, 71.5% for United, and 82.2% for US Airways (Bureau of Transportation Statistics website, October 2012). Assume that 30% of the flights arriving at terminal C are JetBlue flights, 32% are united flights, and 38% US Airways flights.

a. Develop a joint probability table with three rows (the airlines) and two columns (on-time and late).

b. An announcement is made that Flight 1382 will be arriving at gate 20 of terminal C. What is the probability that Flight 1382 will arrive on time?

c. What is the most likely airline for Flight 1382? What is the probability that Flight 1382 is by this airline?

d. Suppose that an announcement is made saying that Flight 1382 will now be arriving late. What is the most likely airline for this flight? What is the probability that Flight 1382 is by this airline?