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Itai Cohen Solutions to Problem Set 1

It’s easiest to begin by calculating the probability p(N) that N people in a room all have different birthdays. The probability of at least two people having the same birthday is then 1 − p(N). Assuming that birthdays are evenly distributed throughout the year, the probability that, in some arbitrary order, the second person in the room does not have the same birthday as the first is given by 364/365. The probability that a third person does not share a birthday with the first two is then 363/365. Continuing in this vein, we find