M 362K, Spring 03, Smith

## Assignment for Monday, September 8

1. Read Section 2.4 and the remainder of p. 35.

- These propositions are important for you to remember and be able to
use in calculating probabilities.
- Study Example 4a to get an idea of how to use these propositions.

- Go through the details of the proofs to be sure you understand what
is going on. If you have not encountered set theory, Venn diagrams, or proofs
before, some extra study in the book by Epp mentioned in the first
day handout would be worthwhile.

2. State Proposition 4.4 in the special case n = 3 and draw a Venn diagram
illustrating the situation.

3. Try #8 on p. 54 again, using what you learned in Section 2.4.

4. Try #9 on p. 54, using what you learned in Section 2.4. (You can check
your answer in the back of the book.)

5. To calculate more probabilities, you will need to learn some counting
techniques. To start on this, read Sections 1.1 and 1.2.

- Be sure to fill in the details of Examples 2c, 2d, and 2e to
include the reasoning, as shown in Examples 2a dn 2b.

6. To test your understanding, try #1 on p. 15 (Check your answer in the
back of the book.)

7. To practice combining the counting techniques from Section 1.2 to probability,
try #1 on p. 61.

- Check your answers in the back of the book.
- Then also calculate the probabilities of each of the events A, B, C,
AB, and ABC, assuming a three-course meal is randomly picked from the cafeteria
offerings.