(Solved): A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C.; 60% of the t ...

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. $20\%$ of the time. For airline $\#2$, these percentages are $15\%$ and $10\%$, 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, 0 late, 1 late, and 2 late.] (Round your answers to fo?t. deccimal places.) airline \#1 airline \#2 airline \#3