A website provides data on the on-time performance of airlines. Suppose that the tables below summarize
data from this website for flights that occurred over a 1 year time period.
(a) The following table summarizes data for flights leaving the Phoenix and Seattle airports for two
airlines, Airline A and Airline B.
On-Time Departure Late Departure Total
Airline A 32,976 4,530 37,506
Airline B 46,762 6,536 53,298
Total 79,738 11,066 90,804
Suppose that one of these flights is selected at random.
(i) What is the probability that the flight had an on-time departure? (Round your answer to
four decimal places.)
(ii) What is the probability that the flight had an on-time departure given that it was an
Airline A flight? (Round your answer to four decimal places.)
(iii) What is the probability that the flight had an on-time departure given that it was an
Airline B flight? (Round your answer to four decimal places.)
(iv) Which airline had the better on-time performance?
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(i) The probability that the flight had an on-time departure is given by the ratio of the number of flights with on-time departure to the total number of flights:
P(on-time departure) = Number of flights with on-time departure / Total number of flights
= 79,738 / 90,804
≈ 0.8771
(ii) The probability that the flight had an on-time departure given that it was an Airline A flight is given by the ratio of the number of flights with on-time departure by Airline A to the total number of Airline A flights:
P(on-time departure | Airline A) = Number of flights with on-time departure by Airline A / Total number of Airline A flights
= 32,976 / 37,506
≈ 0.8795
(iii) The probability that the flight had an on-time departure given that it was an Airline B flight is given by the ratio of the number of flights with on-time departure by Airline B to the total number of Airline B flights:
P(on-time departure | Airline B) = Number of flights with on-time departure by Airline B / Total number of Airline B flights
= 46,762 / 53,298
≈ 0.8776
(iv) Airline A had a slightly better on-time performance, with a higher probability of on-time departure.
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