1) A consultant makes frequent round trips from home in Los Angeles to Washingto
ID: 2922786 • Letter: 1
Question
1) A consultant makes frequent round trips from home in Los Angeles to Washington, DC, 50% of the time the consultant travels on airline #1 , 30% of the time on airline #2, and the remaining trips are made on airline #3. For airline #1, flights into DC. are late 30% of the time and flights into L.A. are late 10% of the time. For airline #2, these percentages are 25% and 20%, whereas for airline #3 the percentages are 40% and 25%. a) What is the probability that the consultant will be late arriving in D.C. on her next trip? b) What is the probability that the consultant will be late at exactly one of D.C. or L.A. on her next trip? c) If we learn that on a particular trip the consultant arrived late at exactly one of the two destinations, what is the (posterior) probability that the consultant was flying on airline #3?Explanation / Answer
a) probabaility that consultant will be late arriving in DC =P(airline 1 and late arriving in DC+airline 2 and late arriving in DC+airline 3 and late arriving in DC) =0.5*0.3+0.3*0.25+0.2*0.4=0.305
b) probability that late in exactly one destination =P(airline 1 and late in exactly one destination+airline 2 and late in exactly one destination+airline 3 and late in exactly one destination)
=0.5*(0.3*(1-0.1)+(1-0.3)*0.1)+0.3*(0.25*(1-0.2)+(1-0.25)*0.2)+0.2*(0.4*(1-0.25)+(1-0.4)*0.25)
=0.365
c)probability of airline 3 given late in exactly one destination =
P(airline 3 and late in exactly one destination)/P(late in exactly one destination)
=0.2*(0.4*(1-0.25)+(1-0.4)*0.25)/0.365 =0.2466
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