2. (8 points, 4+4) Three students, Alice, Betty and Carol are registered for a statistics class. Alice attends 80% of the time, Betty 70% of the time, and Carol 90% of the time. Suppose their absences are independent. On a given day, (1). What is the probability that exactly one of them is in class? (2). What is the conditional probability that Carol is in class, given that at most two of these three students are in class?3. (7 points) Suppose one is rolling a fair six-sided die independently and repeatedly for 10 times. Let X denote the number of rolls that his die score is a prime number, and define Y = 2 - 5X. Find an r.v. Z that standardizes Y