The Nature of Mathematics, 12th Edition
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Section 13.4 Homework Hints

    Problems 1-2
    Look in the book to find a statement of each of these properties.
    Problems 3-4
    Make sure you know these formulas, as well as the conditions for which each applies.
    Problems 5-7
    Use the property of complementary probabilities.
    Problems 8-10
    Since the given events are independent, you can use the multipliplication property of probability.
    Problems 11-13
    Use the addition property of probability.
    Problems 14-19
    Begin with the property of complementary probabilities. Next, be careful to properly order the operations as shown in Example 6.
    Problems 20-22
    Be sure you pay attention to the order of operations. See Example 6.
    Problems 23-28
    See the discussion in the subsection entitled "Independent Events."
    Problems 29-30
    Use the multiplication property of probability as shown in Example 3.
    Problems 31-34
    Use the addition property of probability as shown in Example 5.
    Problems 35-36
    The spinning of each wheel is independent of the spinning and stopping of the other wheels, so you can use the multlipliction property of probability as shown in Example 3.
    Problem 37
    Use the result of Problem 36 for the probabilities, and the definition of expectation to calculate the result.
    Problems 38-39
    See Example 1.
    Problems 40-42
    These are lengthy problems; proceed slowly and look at Example 2.
    Problems 43-44
    See Example 4.

    You might enjoy checking the birthday problem simulation:
    http://www.mste.uiuc.edu/reese/birthday/intro.html#simulation

    Problems 45-46
    Use the multiplication property of probability for these problems. In Problem 48 also use the property of complements.
    Problems 47-48

    These are both lengthy, but important problems. Take your time working through the various parts, as shown in Example 7.
    Problems 49-50

    Build a tree diagram as shown in Example 8.

    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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