This question generalizes the example of "evil-doers" visiting hotels, as in the slides for the 1/9/08 lecture. suppose as before that there are a billion people being monitored for 1000 days. each person has a 1% probability of visiting a hotel on any given day, and hotels hold 100 people each, so there are 100,000 hotels. however, our test for evil-doers is different. we consider a group of p people evil-doers if they all stayed at the same hotel on d different days. derive the formula for the expected number of sets of p people that will be suspected of evil-doing ("false accusations"), assuming that in fact there are no evil-doers, but all people behave at random, following the conditions stated in this problem (1% probability of visiting a hotel, then, find in the list below, the choice that is the best approximation to the correct value for some d and p.
d p f
2 2 2.5 x 10^5
2 3 0.83=1
3 2 10^-1
3 3 3 x 10^-14