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,1late, and 2 late.]

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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,1late, and 2 late.]

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