**Problems 1-6**

There are many problems throughout the text labeled IN YOUR OWN WORDS. These true and false questions are designed to test your basic understanding of the material of this section. Just relax; do not be afraid to give your opinion, but you should do so only after reading this section.

**Problems 7-12**

These problems are designed to help you estimate expectations. Don’t be afraid to guess, check, and then revise, if necessary.

**Problem 13**

Use Figure 13.5 to determine the number of success, and note that there are 36 total possibilities. Finally use the definition of expectation to multiply the amount to be received times the probability of receiving it to find the mathematical expectation.

**Problem 14**

Use the definition of expectation to multiply the amount to be received times the probability of receiving it to find the mathematical expectation as shown in Example 1.

**Problems 15-17**

If there is more than one prize, add the expectation for each prize as shown in Example 2.

**Problem 18**

The mathematical expectation is a fair price to pay for this game.

**Problems 19-20**

For contests with multiple prizes, find the sum of each of the individual expectations as shown in Example 4.

**Problems 21-30**

Use the definition of mathematical expectation; see Example 8.

**Problems 31-34**

In finding the requested expectation, first estimate the portion (written as a fraction) of the circle for each payoff , and then multiply the payoff times that fraction. Do this for each portion and add the results to find the expectation.

**Problems 35-36**

In finding the requested expectation, first estimate the portion (written as a fraction) of the rectangle for each payoff , and then multiply the payoff times that fraction. Do this for each portion and add the results to find the expectation.

**Problem 37**

The number of successes is easy (it is one number), but what is the total number of possibilities? Is is 999 or is it 1,000? After deciding, use the definition of expectation as shown in Example 1.

**Problem 38**

With multiple prizes, find the sum of the expectations for each prize as shown in Example 4.

**Problems 39-42**

Use the definition of mathematical expectation; see Example 7.

**Problems 43-46**

With multiple prizes, add the sum of the individual expectations.

**Problems 47-48**

In these problems, you are finding the expected value. For Problem 47, the expected height is found by multiplying the height and the probability for each table entry. Then add these products as shown in Example 5.

**Problem 49**

This is an interesting example from a real life sweepstakes. Use the definition of mathematical expectation; see Example 4.

**Problem 50**

This game has a cost of playing, so don’t forget to subtract that cost as shown in Example 6. After you find this expected profit, answer the question that is asked.

### Note: Homework Hints are given only for the Level 1 and Level 2 problems.

However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 problems, check some sources for help on the internet (see the LINKS for that particular section. As a last resort, you can call the author at (707) 829-0606.

On the other hand, the problems designated “Problem Solving” generally require techniques that do not have textbook examples.

There are many sources for homework help on the internet.

**Algebra.help**

Here is a site where technology meets mathematics. You can search a particular topic or choose lessons, calculators, worksheets for extra practice or other resources.

**http://www.algebrahelp.com/**

**Quick Math**

This site provides online graphing calculators. This is especially useful if you do not have your own calculator.

**http://www.quickmath.com/**

**The Math Forum** @ Drexel

This site provides an internet mathematics library that can help if you need extra help. For additional homework help at this site, click one of the links in the right-hand column.

**http://mathforum.org/**