The Registrаr оf Pаulsen Pоlytechnic University ("PPU") repоrts thаt 41% of the PPU student body transferred into PPU from a community college. The Registrar also reports that if a student transferred in from a community college, there is a 35% chance that student will get on the Deans List. The top 20% of students are named to the Deans List. (Provide probability answers to 4 decimal places.) (1) If there are 5,000 students at PPU, how many started as freshman at PPU (i.e. did not transfer in)? [ans1] (2) A student comes into the Registrar's office and says s/he started at Illinois Community College. What is the probability that the student will not be on the Deans List? [ans2] (3) What is the probability of being on the Deans List and starting at PPU as a freshman (i.e. did not transfer in)? [ans3] (4) What is the probability that a student transferred into PPU given that the student is on the Deans List? [ans4] (5) What is the probability of not being on the Deans List or not being a former community college student? [ans5]