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A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C.; 40% of...

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Basic Math

A friend who lives in Los Angeles makes frequent consultingtrips to Washington, D.C.; 40% of the time she travels on airline#1, 20% of the time on airline #2, and the remaining 40% of thetime on airline #3. For airline #1, flights are late into D.C. 40%of the time and late into L.A. 15% of the time. For airline #2,these percentages are 30% and 15%, whereas for airline #3 thepercentages are 35% and 20%. If we learn that on a particular tripshe arrived late at exactly one of the two destinations, what arethe posterior probabilities of having flown on airlines #1, #2, and#3? Assume that the chance of a late arrival in L.A. is unaffectedby what happens on the flight to D.C. [Hint: From the tipof each first-generation branch on a tree diagram, draw threesecond-generation branches labeled, respectively, 0 late, 1 late,and 2 late.] (Round your answers to four decimal places.)

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