1. A professor is returning exams to his 35 students. However, the professor is every drunk and gives each student one exam at random. Let X be the number of students who, by chance, receive heir own exam. What is the expected value of X? Show your work.
2. If have three six-sided dice, which look identical to you. Two of the dice are fair (so that they turn up 6 with probability 1/6), and one is loaded in such a way that it comes up 6 with probability 1/2. You take one of the dice at random and roll it. It comes up 6. What is the probability that you rolled the loaded die? Hint: