# Homework Hints 13-4

### 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/

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/

Problem 1
Look in the book to find a statement of this term.
Problems 2-3
Make sure you know these formulas, as well as the conditions for which each applies.
Problem 4
Look in the book to find a statement of this property.
Problems 5-7
Use the property of complementary probabilities.
Problems 8-10
Since the given events are independent, you can use the multiplication property of probability.
Problems 11-12
Since these problems involve operations on three sets, you need to pay attention to the correct order of operations. In Problem 11, first consider the intersection. In Problem 12, consider the complement first. See Example 6.
Problems 13-18
See the discussion in the subsection entitled “Independent Events.”
Problems 19-20
Use the multiplication property of probability as shown in Example 3.
Problems 21-24
Use the addition property of probability as shown in Example 4.
Problems 25-36
These problems involve a stochastic process and a tree diagrams. See Example 8.
Problems 37-38
The spinning of each wheel is independent of the spinning and stopping of the other wheels, so you can use the multiplication property of probability as shown in Example 3.
Problems 39-40
Use the result of Problems 37 and 38 (as requested in each respective problem) for the probabilities, and the definition of expectation to calculate the result.
Problems 41-42
See Example 1.
Problems 43-44
These are lengthy problems; proceed slowly and look at Example 2.
Problems 45-46
Use the multiplication property of probability for these problems. In Problem 46 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.