A friend who lives in Los Angeles makes frequent consulting trips to Washington,
ID: 3071393 • Letter: A
Question
A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C ; S0% of the time she travels on airline1, 30% o the time on ai ne #2, and the emain ng 20% of the time on airline #3. For airline 1 flights are late into D.C 40% o the time and late into LA 10 o the time. For airline #2 these percentages are 25 and 10 whereas or airline #3 the percentages are 30 and 1S% we leam that on a particular trip she arrived late at exactly one of the two destinations, what are the postenor probabilities of having flown on airlines 1,2, and37 Assume that the chance of a late arrival in LA. is unaffected by what happens on the flight to D Hint: From the tip o each first-generation branch on a tree diagram, draw three second-generation branches labeled, respectively, O late, 1 late, and 2 lata. (Round your answers to four decimal places.) airline 02100 airline 42 00K0 airline 00720 P7 Talk to aTuterExplanation / Answer
P(lae on exactly one)=P(airline 1 and late on exactly one)+P(airline 2 and late on exactly one)+P(airline 3 and late on exactly one)
=0.5*0.42+0.3*0.3+0.2*0.36 =0.372
hence given that late on exactly one :
P(airline #1)=0.5*0.42/0.372=0.5645
P(airline #2)=0.3*0.3/0.372=0.2419
P(airline #3)=0.2*0.36/0.372=0.1935
( please revert if any answer comes wrong)