1. In CS 1401 class of size 100, by the time of Test 1, 70% of the students mastered for-loops, 60% mastered while-loops, and 50% mastered both. For a student to pass the test with at least a C, the student must be able to use at least one type of loops. How many students passed the test?
2. At the end of the software engineering class, each group must successfully defend all three parts of their report; if at least one of the parts is unsuccessful, the group needs to redo its reports. Failures in each part are independent. In the first part, 10% of the groups fail, in the second, 20% fail, and in the third, 5% fail. What percentage of the group has to redo their reports?
3. An average student is well-prepared (A-level) for four out of six classes. If an instructor gives surprise quizzes in two of these classes, what percentage of students will get As on both quizzes?
4. Suppose that for each class, 90% of the student are well-prepared (A-level), and different students are independent. What is the probability that in a class of 20, 19 will be well-prepared? What is the probability that the instructor will grade at least 10 papers until he finds a one which does not deserve an A?
5. The quiz has three yes-no questions, testing two (randomly selected) topics out of five that the students studied. A student knows three out of these five topics; for a topic that a student does not know, he gives yes or no answer with equal probability. What are the expected number of mistakes on the quiz? What is the variance of this number?
6. Two students did not prepare well for a quiz. To answer a multiple-choice question with 3 possible answers, each student independently chooses a random number from 1 to 3, with equal probability. Let s be the sum of these numbers, and let d be their difference. What is the probability that s = 3 if d = 1? if d = 0? Are the variables s and d independent? Explain your answer.
7. A company interested in hiring CS graduates give each graduating student a complex test. Only 60% of the students pass this test. When a student fails the test, the company representatives call the next student, etc., until they find a student who can pass this test. On average, how many students will be interviewed before the hiring is made?
8. On average, a programmer makes 2 mistakes a day, with a standard deviation of 2. In a small-size company, with 100 programmers working on different parts of the project, what is a probability that they will make less than 150 mistakes? Use Central Limit Theorem.
9. In a remote CS Department, among 10 faculty, 5 are good teachers and 5 are not so good teachers, and a new student does not know which are good and which are not. What is the probability that, when a student signs for 3 classes, all her professors are good?