Question: A lazy professor gave two tests A and B to a class of n students and assigned marks A i and B i , respectively,

A lazy professor gave two tests A and B to a class of n students and assigned marks A _i and B _i, respectively, to student i, for i = 1, 2, . . . ., n, uniformly and independently at random with values from the set of possible grades 1,2,.., k. What is the probability that some student receives the same grade in both tests?

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