### 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.

- (20 points) In your own words, define "probability".

- (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.

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

- 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.)