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What is the smallest value of c such that the probability

(The birthday problem)

Suppose there are C people, each of whose birthdays (month and day only) are equally likely to fall on any of the 365 days of a normal (i.e., non-leap) year

(a) SupposeC=2 What is the probability that the two people have the same exact birthday?

(b) Suppose C ≤ 2. What is the probability that all C people have the same exact birthday?

(d) What is the smallest value of C such that the probability in part (c) is more than 05? Do you find this result surprising?

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