A friend who lives in Los Angeles makes frequent consulting trips to Washington,
ID: 3307105 • Letter: A
Question
A friend who lives in Los Angeles makes frequent consulting trips to Washington, DC.,50% of the time she travels on airline #1, 20% of the time on airline #2, and the remaining 30% of the time on airline #3. For airline #1, fights are late into D.C. 35% of the time and late into L.A. 25% of the time. For airline #2, these percentages are 40% and 30%, whereas for airline #3 the percentages are 40% and 35%. 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 #37 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 3514 airline #2 12077 airline #3 | 4409Explanation / Answer
probability that she got delayed at exactly one of two destinations
=P( airline #1 and got delayed at exactly one of two destinations+airline #1 and got delayed at exactly one of two destinations+airline #1 and got delayed at exactly one of two destinations)
=0.50*((1-0.35)*0.25+0.35*(1-0.25))+0.2*((1-0.4)*0.3+0.4*(1-0.30))+0.3*((1-0.4)*0.35+0.4*(1-0.35))=0.4455
airline#1 ==0.50*((1-0.35)*0.25+0.35*(1-0.25))/0.4455 =0.4770
airline#2 ==0.2*((1-0.4)*0.3+0.4*(1-0.30))/0.4455 =0.2065
airline#3 =0.3*((1-0.4)*0.35+0.4*(1-0.35))/0.4455 =0.3165
please revert for any clarification required.