**[tippy title=”Problems 1-4″]Problems 1-4**

Look in the book to find a statement of each of these properties.[/tippy]

**[tippy title=”Problems 5-10″]Problems 5-10**

These problems are designed to stimulate your thinking about real world events. You are not expected to calculate these probabilities, but rather to estimate, or even guess, the most appropriate answer.[/tippy]

**[tippy title=”Problems 11-14″]Problems 11-14**

Use the property of complements as shown in Example 1.[/tippy]

**[tippy title=”Problems 15-16″]Problems 15-16**

Use the property of complements as shown in Example 1.[/tippy]

**[tippy title=”Problems 17-18″]Problems 17-18**

Use the fundamental counting principle to determine the number of possibilities and then use the property of complements as shown in Example 2.[/tippy]

**[tippy title=”Problems 19-20″]Problems 19-20**

For odds in favor use success to failure and for odds against use failure to success, as shown in Example 3.[/tippy]

**[tippy title=”Problems 21-22″]Problems 21-22**

You are given the probability and need to find the odds. See Example 5.[/tippy]

**[tippy title=”Problems 23-24″]Problems 23-24**

You are given the odds and need to find the probability. See Example 6.[/tippy]

**[tippy title=”Problems 25-26″]Problems 25-26**

You known the odds and want to find the probability. See Example 7.[/tippy]

**[tippy title=”Problems 27-28″]Problems 27-28**

List the sample space and answer the questions. Also see Example 2.[/tippy]

**[tippy title=”Problems 29-30″]Problem 29-30**

For** part a**, use the fundamental counting principle and the definition of probability. For **part b**, remember that finding the probability of any event does not “remember” the results of previous events.[/tippy]

**[tippy title=”Problem 31″]Problem 31-36**

These are conditional probabilities, so first find the number of possibilities by looking at the altered sample space. For **Problem 31**, P(face card) has *s* = 12 since there are four jacks, four queens, and four kings. Also, *n* = 52 since there are 52 cards. However, for P(face card | jack) alters the sample space to include only the four jacks. For this conditional probability, *s* = 4 and *n* = 4. See Example 8.[/tippy]

**[tippy title=”Problems 37-42″]Problems 37-42**

This is a conditional probability, so you should work with the altered sample space, as shown in Example 10.[/tippy]

**[tippy title=”Problems 43-44″]Problems 43-44**

In **Problem 43**, use the fundamental counting principle to find *s* and *n*.

For *n*, 10*26*26*26*10*10*10.

For *s*, use 10*26*25*24*10*10*10.[/tippy]

**[tippy title=”Problem 45″]Problem 45**

Find the appropriate probabilities and conditional probabilities. See Example 9.[/tippy]

**[tippy title=”Problems 46″]Problems 46**

These are conditional probabilities. See Example 9.[/tippy]

### 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/**

**Ask Dr. Math**

Dr. Math is a registered trademark. This is an excellent site at which you can search to see if your question has been previously asked, or you can send your question directly to Dr. Math to receive an answer.

**http://mathforum.org/dr.math/**

**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/**