A friend who lives in Los Angeles makes frequent consulting trips to Washington,
ID: 3071122 • Letter: A
Question
A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C. ; 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 fli hts are late into D C 40% of the time and late into LA 15% of the time Forai ne 2 these percentages are 4 09 and 30 whereas fr airline #3 the percentages are 35% and 20% f we learn that on a particular trip she am ed ate at exactly one of the two estination at a e e posteno obabilite in flown on airlines #1 :2, and #37 Assume that the chance of a late am al in LA is unaffected by what happens on the ght to DC. H t: From e p of each inst generation branch on a tree diagram, draw three second-generation branches labeled, respectively, 0 late, 1 late, and 2 late.] (Round your answers to four decimal places.) airline #1 0.4805 airline #2 2356 airline #3 02408Explanation / Answer
P(late 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*(0.4*(1-0.15)+(1-0.4)*0.15)+0.2*(0.4*(1-0.3)+(1-0.4)*0.3)+0.3*(0.35*(1-0.2)+(1-0.35)*0.2)
=0.43
hence given late on exactly one:
P(airline 1)=0.5*(0.4*(1-0.15)+(1-0.4)*0.15)/0.43=0.5
P(airline 2)=0.2*(0.4*(1-0.3)+(1-0.4)*0.3)/0.43=0.2140
P(airline 3)=0.3*(0.35*(1-0.2)+(1-0.35)*0.2)/0.43=0.2860