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 second-generation branches labeled, respectively, 0 late, 1 late, and 2 late.]

Problem 68E Answer: Step1: We have 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%. Our goal is to find, 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 #3Assume that the chance of a late arrival in L.A. is unaffected by what happens on the flight to D.C. Step2: Let B = L M , that the flight was not late into D.C. and not late into L.A. The event that the 0 trip was late on exactly one leg B = (LM )(L M), that it was late int D.C. but on time into 1 L.A. or it was on time into D.C. and late into L.A. The event that there were two late legs B 2LM, that the flight was late into D.C. and late into L.A. Thus, since conditional probabilities are probabilities and using the assumption that L and...