I have not been able to understand following text from bookThere 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 daysHow 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 followingThus, the chance that they will visit the same hotel onone given day is 10−9. The chance that they will visit the same hotel on twodifferent given days is the square of this number, 10−18. Note that the hotelscan be different on the two days.This probability calculation is also not clear to me. Any help will great. Thanks

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rass1k6s · Accepted Answer

We are studying       10    9   people.On any day, we should expect 1% of them to visit a hotel, which would be       10    9    ⋅      10          −      2        =      10    7   of them deciding to visit a hotel.Each hotel can hold   100  =      10    2   people, to handle then 107 people, we need             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 105 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      .

I have not been able to understand following text from book There are one billion people who might

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