A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C.; 60% of the time she travels on airline #1, 20% 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. 40% of the time and late into L.A. 10% of the time. For airline #2, these percentages are 30% and 25%, whereas for airline #3 the percentages are 20% and 10%. If we learn that on a particular trip she arrived late at exactly one of the two destinations, what are
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A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C.; 60% of the time she travels on airline #1, 20% 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. 40% of the time and late into L.A. 10% of the time. For airline #2, these percentages are 30% and 25%, whereas for airline #3 the percentages are 20% and 10%. 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.
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