Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 1. There are three Advanced Statistics teachers at Rene Descartes High. Students enrolled in the course are randomly assigned to one of the teachers' classes-Mr. Root Canal, Ms. Primenator, and Mrs. Zero-with probabilities 0.5, 0.3, and 0.2, respectively. Mr. Root Canal fails 60% of his students, 45% of Ms. Primenator's students fail, while Mrs. Zero lives up to her name by failing 35% of her students. (a) Find the probability that a randomly selected Advanced Statistics student from Rene Descartes High fails the course. Show your work. (A tree diagram will help) (b) Billy is taking Advanced Statistics at Rene Descartes High. Given that Billy failed the course, find the probability that he had Mr. Root Canal. Show your work. (c) There is a group of 7 friends that are all taking Advanced Statistics. What is the probability that at least one of them has Mrs. Zero