Question

The Census Bureau says that the 10 most common names in the United States are (in order) Smith, Johnson, Williams, Brown, Jones, Miller, Davis, Garcia, Rodriguez, and Wilson. These names account for 9.6% of all U.S. residents. Out of curiosity, you look at the authors of the textbooks for your current courses. There are 9 authors in all. Would you be surprised if none of the names f these authors were among the 10 most common? (Assume that authors' names are independent and follow the same probability distribution as the names of all residents.)

Answer 1

9.6% that a us residents last name is one of those 10 common last names 90.4% that a us resident DOESNT have one of those 10 common last names

So we want to know what is the probabilty that all 8 authors dont have one of those 10 common last names. For each of teh 8 authors there is the probability of .904 that they dont have one of those 10 last names so

(.904)8=.446