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CHAPTER
9 PROBABILITY LEARNING
OBJECTIVES Upon
completion of this chapter, you should be able to do the following: 1.
Apply the basic concepts of probability. 2.
Solve for probabilities of success and failure. 3.
Interpret numerical and mathematical expectation. 4.
Apply the concept of compound probabilities to independent, dependent, and
mutually exclusive events. 5.
Apply the concept of empirical events. INTRODUCTION The
history of probability theory dates back to the 17th century and at that time
was related to games of chance. In the 18th century the probability theory was
known to have applications beyond the scope of games of chance. Some of the
applications in which probability theory is applied are situations with
outcomes such as life or death and boy or girl. Statistics and probability are
currently applied to insurance, annuities, biology, and social investigations. The
treatment of probability in this chapter is limited to simple applications.
These applications will be, to a large extent, based on games of chance, which
lend themselves to an understanding of basic ideas of probability. BASIC
CONCEPTS If
a coin were tossed, the chance it would land heads up is just as likely as the
chance it would land tails up; that is, the coin We define probability as the ratio of the different
number of ways a trial can succeed (or fail) to the total number of ways in
which it may result. We will let p represent the probability of success
and q represent the probability of failure. One commonly misunderstood concept of probability is the
effect prior trials have on a single trial. That is, after a coin has been
tossed many times and every trial resulted in the coin falling heads up, will
the next toss of the coin result in tails up? The answer is "not
necessarily" and will be explained later in this chapter. 
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