A friend who lives in Los Angeles makes frequent consulting trips to Washington, DC; 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 DC 30% of the time and late into LA 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? 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.
A friend who lives in Los Angeles makes frequent consulting trips to Washington, DC; 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 DC 30% of the time and late into LA 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? 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.
MATLAB: An Introduction with Applications
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Transcribed Image Text:A friend who lives in Los Angeles makes frequent consulting trips to Washington, DC;
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 DC 30% of the time and late into LA 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?
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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Step 1: Write the given information.
VIEWStep 2: Construct the tree diagram and determine the probabilities for all the branches.
VIEWStep 3: Determine probability that on a particular trip she arrived late at exactly one of two destinations.
VIEWStep 4: Determine the posterior probability of having flown on airlines #1, #2 and #3.
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