Suppose a large metropolitan university has 10,000 students and that the risk faced by each student of getting mononucleosis at some point during a term is .0005. Assume that whether one student gets mono has no effect on whether others get it.

(a) What is the mean number of students expected to get mono during a term?

(b) If the assumptions continue to hold, what is the probability that no students will get mono in a term? Give three decimal places.

(c) One of the dorms at this university has averaged 1.2 cases of mono per term over the past decade, sometimes more, sometimes less. At the end of an additional term they find they had 4 cases. What is the probability they would have had at least this many if the same underlying risks had remained the same? Is this evidence that an outbreak has increased the risk of mono in this dorm? Give your answer to three decimal places.