### MATH 318, Chapter 2 Quiz

Name:
You may use a calculator on this quiz. You may not use a cell phone or computer. If you wish partial credit for incorrect answers, 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.
1. (20 points) In your own words, define "probability".

2. (20 points) Are the events "the numbers shown on two dice add up to 5" and "The first die shows the number 3" dependent or independent?  Explain your answer.

3. (20 points) Give an example of two mutually exclusive events.

4. Shown below is a contingency table describing the weather over 200 days.
 Sunny Cloudy Total Temperature Above Freezing 70 50 120 Temperature Below Freezing 60 20 80 Total 130 70 200

a) (20 points) Create a joint probability table for this data.

b) (20 points) Suppose that on a randomly selected day the temperature was above freezing.  What is the probability that that was a sunny day?

Bonus (5 points) What is Bayes' Theorem? (There is more than one correct answer to this question.)