A survey is being conducted in a city with 1 million residen

A survey is being conducted in a city with 1 million residents. It would be far too expensive to survey all of the residents, so a random sample of size 1000 is chosen (in practice, there are many challenges with sampling, such as obtaining a complete list of everyone in the city, and dealing with people who refuse to participate). The survey is conducted by choosing people one at a time, with replacement and with equal probabilities.

(a) Explain how sampling with vs. without replacement here relates to the birthday problem.

(b) Find the probability that at least one person will get chosen more than once.

Solution