. A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C.; 50% of
the time she travels on airline #1, 30% of the time on airline #2, and the remaining 20% of the
time on airline #3. For airline #1, flights are late into D.C. 30% of the time and late into L.A. 10%
of the time. For airline #2, these percentages are 25% and 20%, whereas for airline #3 the
percentages are 40% and 25%. If we learn that on a particular trip she arrived late at exactly one
of the two destinations, what are the posterior probabilities of having flown on airlines #1, #2, and
#3? Assume that the chance of a late arrival in L.A. is unaffected by what happens on the flight to
D.C. [Hint: From the tip of each first-generation branch on a tree diagram, draw three secondgeneration
branches labeled, respectively, 0 late, 1 late, and 2 late.]