A friend who lives in Los Angeles make frequent consulting trips to Washington D.C.; 50% of the time she travels on airplane airline #1, 30% of the time on airplane airline #2 and the remaining 20% of the time on an airplane airline #3. For airline #1, flights are late into D.C. 30% of the time are late into L.A. 10% of the time. For airline #2, these percentages are 25% and 20%, where is for airline #3 the percentages are 40% and 25%. If you 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 airline #1, #2, #3? Assume that the chance of the 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 second-generation branches labeled, respectively, 0 late, 1 late, and 2 late.]

Show me a vann diagram and all the necessary steps and details from scratch as much as possible please. Thank you