The Nature of Mathematics, 12th Edition
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Section 13.3 Homework Hints

    Problems 1-2
    Look in the book to find a statement of each of these properties.
    Problem 3
    Begin by asking how many different locations are there for the first move. Then, repeat for the second move. Now, using the fundamental counting principle, how many ways can you do the first two moves? After you have done this, you should be able to answer the question. Be sure to give reasons.
    Problems 4-5
    Look in the book to find a statement of these ideas.
    Problems 6-11
    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.
    Problems 12-15
    Use the property of complements as shown in Example 1.
    Problems 16-17
    Use the property of complements as shown in Example 1.
    Problems 18-19
    Use the fundamental counting principle to determine the number of possibilities and then use the property of complements as shown in Example 2.
    Problems 20-21
    For odds in favor use success to failure and for odds against use failure to success, as shown in Example 3.
    Problems 22-23
    You are given the probability and need to find the odds. See Example 5.
    Problems 24-25
    You are given the odds and need to find the probability. See Example 6.
    Problems 26-27
    You known the odds and want to find the probability. See Example 7.
    Problems 28-29
    List the sample space and answer the questions. Also see Example 2.
    Problem 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.
    Problems 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.

    Problems 37-42
    This is a conditional probability, so you should work with the altered sample space, as shown in Example 10.
    Problems 43-45
    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.
    Problem 46

    Use the fundamental counting principle to find n. Find s by thinking about the possibilities. After you know n and s, use the formula

                                                           s + f = n

    to find f. The odds in favor are s to n.

    Problem 47

    Find the appropriate probabilities and conditional probabilities.  See Example 9.
    Problems 48-49

    These are conditional probabilities. See Example 9.

    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/

    Mathematics Home Page
    Access the Clemens and Alcuins Library of CSB/SJU and find one of the world's best collections of mathematical internet sites.
    http://library.csbsju.edu/rqs.phtml?subject_id=32

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