Suppose that Social Security numbers were issued uniformly at random, with replacement. That is, your Social Security number would consist of just nine randomly generated digits, and no check would be made to ensure that the same number was not issued twice. Sometimes, the last four digits of a Social Security number are used as a password. How many people would you need to have in a room before it was more likely than not that two had the same last four digits? How many numbers could be issued before it would be more likely than not that there is a duplicate number? How would you answer these two questions if Social Security numbers had 13 digits? Try to give exact numerical answers.