Suppose that the probability of getting an A+ in a particular course is 0.08, and assume that the all student grades are independent. If you randomly sample 20 students taking the course; (a) Find the expected number of students that will get an A+, and the standard deviation of number of students that will get an A+. Find the probability that no student gets an A+. ) c) Find the probability that at least 3 students get an A+. ) Find the probability that between 3 and 5 students get an A+ (inclusive). ) If (in a different course), the probability that no students out of 20 got an A+ was 0.1000, what was the probability of a success? You may assume that all students were independent, and the probability of an A does not change. Twelve people (three from each of four families) participate in a raffle drawing at a fair. Four of the twelve are randomly chosen (no person is allowed to be chosen more than once) as winners. (a) Find the probability that exactly one of the winners comes from each of the families. (b) Would it be unusual for all of the members of one family to be winners? 1 (c) How would your answer in (a) differ if people were allowed to win more than once