Two pilots (X and Y) are assigned to a flight from Atlanta to Chicago. Both need to be in the airport by 9pm, otherwise the flight will be delayed. Earlier in the day, X flies from Cedar Rapids and is scheduled to land at 8:30pm. Y arrives from Minneapolis and is scheduled to land at 8:30pm as well. Both flights are running late, and the delays are well modeled by exponential distribution with averages 20 minutes for the flight from Cedar Rapids and 15 minutes for the flight from Minneapolis. In detail please solve the following: i. Find probability that X lands by 9pm. ii. Find probability that flight to Chicago will have to be delayed. iii. Suppose that you have another pilot who could be assigned to Chicago flight, so you only need either X or Y. Find probability that flight to Chicago will depart on time.
Two pilots (X and Y) are assigned to a flight from Atlanta to Chicago. Both need to be in the airport by 9pm, otherwise the flight will be delayed. Earlier in the day, X flies from Cedar Rapids and is scheduled to land at 8:30pm. Y arrives from Minneapolis and is scheduled to land at 8:30pm as well. Both flights are running late, and the delays are well modeled by exponential distribution with averages 20 minutes for the flight from Cedar Rapids and 15 minutes for the flight from Minneapolis. In detail please solve the following:
i. Find
ii. Find probability that flight to Chicago will have to be delayed.
iii. Suppose that you have another pilot who could be assigned to Chicago flight, so you only need either X or Y. Find probability that flight to Chicago will depart on time.
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