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Problem
One reason why the answer to the birthday problem is surprising is that it differs from the answers to apparently related questions. For the following, suppose that there are n people in the room, and disregard leap years.
(a) What is the probability that someone in the room will have a birthday on a random date drawn from a hat?
(b) What is the probability that at least two people in the room will have that same random birthday?
(c) If we choose one person and find that person's birthday, what is the probability that someone else in the room will share the birthday?
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