A traveller decides to go on vacation to Mexico. There are no direct flights from the traveller's city, and therefore her flight to Mexico will require a connection. The traveller is considering one of three different airlines to fly to Mexico: Airline A, Airline B, or Airline C. Because of the connection, the traveller's luggage is required to move from one airplane to another, as is the case with all connecting flights. After a Google-search, she has discovered that Airline A will misplace 12% of all luggage it transfers, Airline B will misplace 4% of all luggage it transfers, and Airline C will misplace 9% of all luggage it handles. Historically, she has flown with Airline A 27% of the time, with Airline B 48% of the time, with the remaining percentage of her flights to Mexico being with Airline C. a) What is the probability that she arrives in Mexico, her luggage will arrive with her. That is, find the probability that this traveller's luggage will be not be misplaced. b) If her luggage was misplaced, what is the probability that she flew with Airline A?
a) P( she arrives in Mexico, her luggage will arrive with her) =P(travel by A)P(not missing luggage)+P(B)*P(not missing)+P(C)*P(not missing)=0.88*0.27+0.96*0.48+0.91*(1-0.27-0.48)=0.9259
b) P(lugguage misplaced) = 1-P(luggage arrive) = 1-0.9259=0.0741
P(flew with airline A|luggage misplaced) = P(airline A and luggage misplaced)/P(luggage misplaced) = 0.12*0.27/0.0741 = 0.4372
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A traveller decides to go on vacation to Mexico. There are no direct flights from the...
Twenty percent of all the flights between two cities: City A and City B take place through an airline called Airline A. The records have shown that Airline A misplaces the luggage for 10% of its customers, but in 90% of these cases, the lost luggage is found. Using this information, if we randomly select a customer who flew from City A to City B, what is the probability that the customer flew on Airline A, had their luggage misplaced,...