The Great Air Commuter Service Company started in 1984 to pro-vide efficient and inexpensive commuter travel between Boston and New York City. People in the airline industry know Peter Wilson, the principal owner and operating manager of the company, as “a real promoter.” Before founding Great Air, Peter operated a small regional airline in the Rocky Mountains with varying success. When Cascade Airlines offered to buy his company, Peter decided to sell and return to the East.
Peter arrived at his office near Fenway Park in Boston a little later than usual this morning. He had stopped to have a business breakfast with Aaron Little, his long-time friend and sometime partner in various business deals. Peter needed some advice and through the years has learned to rely on Aaron as a ready source, no matter what the subject.
Required Tasks:
1. Assume that there are 365 days in a year (in other words, there is no leap year). Also assume there is an equal probability of a passenger’s birthday falling on any one of the 365 days. Calculate the probability that there will be at least one birthday match for a flight containing exactly 20 passengers.
2. Repeat (1) above for a flight containing 30 passengers and a flight containing 40 passengers. Again, it will be easier to compute the probabilities of one or more matches if you first compute the probability of no birthday matches.
3. Assuming that each of the six daily flights carries 20 passengers, calculate the probability that the airline will have to award two or more major prizes that month. (Hint: It will be easier to calculate the probability of interest by first calculating the probability that the airline will award one or fewer prizes in a month).