65. 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, ights 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 own on airlines

#1, #2, and #3? Assume that the chance of a late arrival in L.A. is unaffected by what happens on the ight to D.C. (Hint: From the tip of each rstgeneration branch on a tree diagram, draw three second-generation branches labeled, respectively, 0 late, 1 late, and 2 late.)