Phoenix is a hub for a large airline. Suppose that on a particular day, 8,000 passengers arrived in Phoenix on this airline. Phoenix was the final destination for 1,800 of these passengers. The others were all connecting to flights to other cities. On this particular day, several inbound flights were late, and 480 passengers missed their connecting flight. Of these 480 passengers, 75 were delayed overnight and had to spend the night in Phoenix. Consider the chance experiment of choosing a passenger at random from these 8,000 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. Fifty passengers selected at random from the 8,000 passengers who arrived in Phoenix on the day described above will be contacted for the survey. The airline knows that the survey results will not be favorable if too many people who were delayed overnight are included. Write a few sentences explaining whether or not you think the airline should be worried, using relevant probabilities to support your answer.