Suppose that there is a class of n students. Homework is to be returned to students,...

Suppose that there is a class of n students. Homework is to be returned to students, but the students’ homework assignments have been shuffled and are distributed at random to students.

a) Calculate the probability that you get your own homework back. (I think it is 1/n)

b) Suppose that I tell you that another student, Betty, got her own homework. Does this change the probability that you get your own homework, and if so what is the new probability? (I think it is now 1/(n-1)

c) What is the expected number of students who receive their own homework?

d) Find an approximation for the distribution of the random variable denoting the number of students who receive their own homework in the limit of large n.

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