(Moderator's note: thread moved from "Set Theory, Logic, Probability, Statistics ") "A lecturer gives spot quizzes in randomly selected classes. In those quizzes he asks questions from the material covered in the previous class. From experience it is known that a student has 0.85 chance of passing the quiz if the student was present in the last class. For a student who was absent last class, that chance is only 0.20. There are 30 students in the class today. Five of those students were absent in the last class. The lecturer has given a spot quiz today." What is the probability that more than 25 students will pass?