There are currently =29 students in this class. Suppose that after grading your homework we run a faulty script and send you an assignment chosen uniformly at random from all the assignments, where sampling is with replacement (that is, it is possible for multiple students to get the same assignment). [I promise, we won't really do this, at least not for now!].

1. What is the probability that you get your own assignment?
2. What is the expected number of students who will get their own assigments?
3. What is the probability that everyone gets their own assignment?
4. Write down the estimates of the probability of everyone getting their own (correct) assignments that you would obtain by applyng Markov inequality, Chebyshev inequality, and the Hoeffding bound.