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. 25% of the time. For airline #2, these percentages are 25% and 10%, whereas for airline #3 the percentages are 40% and 30%. 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 second-generation branches labeled, respectively, 0 late, 1 late, and 2 late.]