A friend who lives in Los Angeles makes frequent consultingtrips to Washington, D.C.; 50% of the time shetravels on airline #1, 30% 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. 30% of the time and late intoL.A. 10% of the time. For airline #2, these percentagesare 25% and 20%, whereas for airline #3 the percentagesare 40% and 25%. If we learn that on a particular trip shearrived late at exactly one of the two destinations, whatare the posterior probabilities of having flown on airlines#1, #2, and #3? Assume that the chance of a late arrival inL.A. is unaffected by what happens on the flight to D.C.[Hint: From the tip of each first-generation branch on atree diagram, draw three second-generation brancheslabeled, respectively, 0 late, 1 late, and 2 late.]
A friend who lives in Los Angeles makes frequent consulting
trips to Washington, D.C.; 50% of the time she
travels on airline #1, 30% 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. 30% 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 40% and 25%. 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, 0 late, 1 late, and 2 late.]
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