Suppose the number of students who register for a certain class each semester can be modeled by a Poisson distribution with average 10. Suppose further that each student passes the class with probability 90% independently of how the other students fare. a) What is the probability that less than 5 students register? What is the prob- ability that at least one student registers? b) Given that n students have registered for the course, what is the probability that none of them pass? c) Find the probability that no student will pass the class next semester. [Give answer as a decimal accurate to 4 places]