Question 15: There are three major air carriers with flights from Boston to Los
ID: 3069734 • Letter: Q
Question
Question 15: There are three major air carriers with flights from Boston to Los Angeles: 55% of all passengers take American Airlines, 16% take American West, and 29% take United Airlines. Data from 2005 indicate 23% of all American Airlines flights from Boston to Los Angeles are late, 27% of American West flights from Boston to Los Angeles are late, and 24% of United Airlines flights from Boston to Los Angeles are late. Suppose a passenger taking a flight from Boston to Los Angeles is randomly selected a. What is the probability that the passenger takes American Airlines and is late? b. What is the prod le c. Suppose the passenger arrives late. Which airline did the passenger most likely fly?Explanation / Answer
a)P(takes American Airline and late)=P(American Airline)*P(late|American Airline)=0.55*0.23=0.1265
b) P(late)=P(American Airline)*P(late|American Airline)+P(American west)*P(late|American west)+P(United Airline)*P(late|U nited Airline)=0.55*0.23+0.16*0.27+0.29*0.24=0.2393
c)
P(American Airline|late)=P(American Airline)*P(late|AmericanAirline)/P(late)=0.55*0.23/0.2393=0.5286
P(American west|late)=0.16*0.27/0.2393 =0.1805
P(United Airline|late) =0.29*0.24/0.5286 =0.2908
from bove we can see that probabiltiy of American Airline is highest given passengers arrive late