Consider a class with N students. Calculate the following probabilities: (it may help to answer the question for N = 2 initially, and work your way up. Also assume that there are 365 days in the year) (a) What is the probability that every one in the class has a birthday on January 1st. (b) What is the probability that everyone in the class has the same birthday. (c) What is the probability that for each of the ?rst N ≤ 365 days of the year, exactly one student has a birthday on that day. (d) What is the probability that you have a birthday on one of the ?rst N ≤ 365 days of the year (e) Assuming you are in the class, what is the probability that another student has the same birthday as you?