1. (2 Points) As a company manager, there is a 0.45 probability that you will be promoted this year. There is a 0.72 probability that you will get a promotion, or a raise, or both. The probability of getting a promotion and a raise is 0.25.
   1. What is the probability that you won't be promoted this year?
   2. If you get a promotion, what is the probability that you will also get a raise? What is the probability that you will get a raise?
   3. Are getting a raise and being promoted independent events? Explain using probabilities.
   4. Are these two events mutually exclusive? Explain using probabilities.

1. (3 Points) The American Council of Education reported that 48% of college freshmen earn a degree and graduate within five years. Assume that graduation records show women make up 50% of the students who graduated within five years, but only 45% of the students who did not graduate within five years. The students who had not graduated within five years either dropped out or were still working on their degrees.
   1. Let A1 = the student graduated within five years;

A2 = the student did not graduate within five years;

W = the student is a female student.

Using the given information, what are the values for P(A1), P(A2), P(W|A1), and P(W|A2)?

1. What is the probability that a female student will graduate within five years?
2. What is the probability that a male student will graduate within five years?
3. Given the preceding results, what are the percentage of women and the percentage of men in the entering freshman class?

1. (3 Points) Two percent of the parts produced by a machine are defective. Twenty parts are selected at random.
   1. What is the probability that exactly 3 parts will be defective?
   2. What is the probability that the number of defective parts will be more than 2 (not including 2) but fewer than 6 (not including 6)?
   3. What is the probability that 4 parts or more will be defective?
   4. What is the expected number of defective parts?
   5. What is the variance for the number of defective parts?