You may use a calculator and a sheet of notes on this quiz. You may not use a cell phone or computer. Please show your work carefully and give justifications for your answers. If you find that you are spending a lot of time on one problem, leave it blank and move on to the next. There are questions on both sides of this quiz paper.

- Give an example of a probability estimate that was generated using the relative frequency method.
- A class has 15 men and 10 women. Three of the women have names starting in A. Two of the men have names starting in A.
a) (15 points) Create a crosstabulation or joint probability table for this data.

b) (15 points) What is the probability that a student selected at random from this class has a name starting in A? Show your work.

c) (20 points) Suppose that you know that a student's name does not start with A. What is the probability that that student is a man? Show your work.

- (20 points) In another class at BSU, 60% of the students are women and 40% are men. Suppose that 5% of women's names at BSU start with A and 10% of men's names start with A. If you know that the name of a person in that class starts with A, what is the posterior probability that that student is a woman?
- (10 points) Use the formula for calculating conditional probability to explain why P(A) = P(B) whenever P(A | B) = P(B | A). (Hint: Start from the fact that the conditional probabilities are equal and work to the conclusion that P(A) = P(B).)
**Bonus**(5 points) If two events are mutually exclusive, can they also be independent? Give an example or explain why not.