I am reading a chapter of book Mining of Massive Data Sets book is available here http://www.mmds.org Chapter 1 http://infolab.stanford.edu/~ullman/mmds/ch1.pdf Now in Section 1.2.3 An example of Bonferroni's principle has been given. I have not been able to understand following text from book
There are one billion people who might be evil-doers. 2. Everyone goes to a hotel one day in 100. 3. A hotel holds 100 people. Hence, there are 100,000 hotels – enough to hold the 1% of a billion people who visit a hotel on any given day. 4. We shall examine hotel records for 1000 days
How do they come to conclusion that there are 100,000 hotels? How are 100,000 hotels enough to hold 1% of a billion people.
Then in the same example they have mentioned following
Thus, the chance that they will visit the same hotel on one given day is 10−9. The chance that they will visit the same hotel on two different given days is the square of this number, 10−18. Note that the hotels can be different on the two days.
This probability calculation is also not clear to me. Any help will great. Thanks