Question

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. 20% 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 30% and 15%. 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, O late, 1 late, and 2 late.] (Round your answers to four decimal places.) airline #1 airline #2 airline #3

Answer 1