Let n greaterthanorequalto 2 be an integer and consider a group P_1, P_2, ..., P

Question

Let n greaterthanorequalto 2 be an integer and consider a group P_1, P_2, ..., P_n of n people. Each of these people has a uniformly random birthday, which is independent of the birthdays of the other people. We ignore leap years; thus, the year has 365 days. Define the random variable X to be the number of unordered pairs {P_i, P_j} of people that have the same birthday. What is the expected value E(X) of X? (a) 1/365 middot (n 2) (b) (1/365)^2 middot (n 2) (c) 1/365 middot (n^2) (d) (1/365)^2 middot (n^2)

Explanation / Answer

Here, we have n>=2 and the group in question has P1, P2, ...., Pn of n people. We thus have the answer as

The correct answer for this would be a) 1/365*(n 2)

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