# Bonferroni’s Principle discussed in Mining of Massive Data Sets book

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

We are studying $$10^9$$ people.

On any day, we should expect $$1\%$$ of them to visit a hotel, which would be $$10^9 \cdot 10^{-2}=10^7$$ of them deciding to visit a hotel.

Each hotel can hold $$100=10^2$$ people, to handle then $$10^7$$ people, we need $$\frac{10^7}{10^2}=10^5$$ hotels in the market.

Now for your second question, the probability that two particular people would decide to visit some hotel on the same day independently is $$(10^{-2})^2=10^{-4}$$. Remember that we have $$10^5$$ hotels, hence the chance of visiting the same hotel on the same day would be $$(10^{-5})(10^{-4})=10^{-9}$$. The probability that they will visit the same hotel on $$2$$ different day would then be $$(10^{-9})^{2}=10^{-18}$$.

• Thanks for coming to answers actually I am not clear with the probability thing I have forgotten every thing in probability. So I am not able to understand the explanation why the probability of 2 people to visit some hotel on same day independently will be (10^-2)2 = 10^-4 and the things after that I am not able to follow. How did you make expressions here in stackoverflow for maths of numbers like number to power some thing etc. Do you use some Latex here? – political science Sep 14 at 16:25
• I checked your web page I get error web.mit.edu/stgoh/www/mypage/siongthye.html the page not found error I can share a screenshot. Don't know how to do so here. – political science Sep 14 at 16:38
• We use mathjax on this site on type maths, it is like latex. For two independent event, we have $P(A \cap B)=P(A)P(B)$. I am assuming that they pick the hotel uniformly. Yup, they removed my website earlier this year after I graduated. – Siong Thye Goh Sep 14 at 16:42
• Please give me some probability tutorial link which is easy and can cover data mining related things. I have an exam of this subject after 36 hours and I have not studied any thing I need to cover up from Chapter 1 to Chapter 8 and the course seems to be a lot more than I can cover before exam. Any question paper or solutions you encountered for this subject that I can practise. – political science Sep 14 at 17:14
• what is crucial is the foundation. here is a video on independent events. 8 chapters seems a lot to be covered in $2$ days. I have forgotten most details for this type of class so I can't help much. – Siong Thye Goh Sep 14 at 17:35