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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.


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.


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 has no more reason to land heads up than it has to land tails up. Every toss of the coin is called a trial.

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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