6.18 Phoenix is a hub for a large airline. Suppose that on a particular day, 8000 passengers arrived in Phoenix on this airline. Phoenix was the final destination for 1800 of these passengers. The others were all connecting to flights to other cities. On this particular day, several inbound flights were late, and 480 connecting passengers missed their connecting flight and were delayed in Phoenix. Of the 480 who were delayed, 75 were delayed overnight and had to spend the night in Phoenix. Consider the chance experiment of choosing a passenger at random from these 8000 passengers. Compute the following probabilities:

a. the probability that the selected passenger had Phoenix as a final destination.

b. the probability that the selected passenger did not have Phoenix as a final destination.

c. the probability that the selected passenger was connecting and missed the connecting flight.

d. the probability that the selected passenger was a connecting passenger and did not miss the connecting flight.

e. the probability that the selected passenger either had Phoenix as a final destination or was delayed overnight in Phoenix.

f. An independent customer satisfaction survey is planned. The company carrying out the survey plans to contact 50 passengers selected at random from the 8000 passengers who arrived in Phoenix on the day described above. The airline knows that the survey results will not be favorable if too many people who were delayed overnight are included in the survey. Should the airline be worried?

Write a few sentences explaining whether or not you think the airline should be worried, using relevant probabilities to support your answer.