2. due to a technology glitch, an airline has overbooked the number of passengers in economy class on a flight from
new york city to los angeles. currently, there are 150 passengers who have economy class tickets, but there are
only 141 seats on the plane. there are two seats available in first class and one seat available in business class.
a. explain how the ticket agent could use a random number generator to make a fair decision in moving some
passengers to either the first- or business-class sections of the plane and to rebook the extra passengers to a
later flight.
b. is there any other way for the ticket agent to make a fair decision? explain.

a) Let r be a random number generated in the interval (0, 1). If we multiply r by n we will obtain a random number in the interval (0, n). We take the integer part of r*n+1 to generate a random integer between 1 and n.

Suppose that the tickets are numered and we order them ascendently. We generate a random integer K from 1 to 150 and we take the Kth ticket in the ordered list of tickets to design the first passanger to go to first class. We put the remaining tickets in order and pick another one by selecting, this time, a number from 1 to 149 (because we removed one ticket). Then we do this a third time to pick a passanger to the business class by picking a number from 1 to 148 and selecting the respective ticket.

After we select the 3 affortunate passangers, we select other 6 more using this same method to rebook them to a later flight.

b) You may move randomly two passangers from business class to first class and then move 3 passangers from economy class to business class, thus, a passanger that pay for a more economic ticket wont be in a more expensive site. Also, if the tickets are numered in order of purchase, then you can, instead of making a random selection, move only passangers with the lowest numbers.