Discuss each of the following topics in class or review the topics on your own. Then write a brief but complete essay in which you summarize the main points. Please include formulas as appropriate.
1. Discuss the following concepts and give examples from everyday life in which you might encounter each concept. 

(a) Sample space.
(b) Probability assignment to a sample space. In your discussion, be sure to include answers to the following questions.
(i) Is there more than one valid way to assign probabilities to a sample space? Explain and give an example.
(ii) How can probabilities be estimated by relative frequencies? How can probabilities be computed if events are equally likely?
2. Discuss the concepts of mutually exclusive events and independent events. List several examples of each type of event from everyday life.
(a) If A and B are mutually exclusive events, does it follow that A and B cannot be independent events? Give an example to demonstrate your answer.
(b) Discuss the conditions under which P(A and B) = P(A) = P(B) is true. Under what conditions is this not true?
(c) Discuss the conditions under which P(A or B) = P(A) = P(B) is true. Under what conditions is this not true?
3. Although we learn a good deal about probability in this course, the main emphasis is on statistics. Write a few paragraphs in which you talk about the distinction between probability and statistics. In what types of problems would probability be the main tool? In what types of problems would statistics be the main tool? Give some examples of both types of problems. What kinds of outcomes or conclusions do we expect from each type of problem?