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A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C.; 50% of...

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Basic Math

A friend who lives in Los Angeles makes frequent consultingtrips to Washington, D.C.; 50% of the time she travels on airline#1, 20% of the time on airline #2, and the remaining 30%of the timeon airline #3. For airline #1, flights are late into D.C. 15% ofthe time and late into L.A. 10% of the time. For airline #2, thesepercentages are 40% and 30%, whereas for airline #3 the percentagesare 35% and 20%. If we learn that on a particular trip she arrivedlate at exactly one of the two destinations, what are the posteriorprobabilities of having flown on airlines #1, #2, and #3? Assumethat the chance of a late arrival in L.A. is unaffected by whathappens on the flight to D.C. [Hint: From the tip of eachfirst-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.)

airline #1    
airline #2    
airline #3    

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