The theory of mathematical probability is a little over three hundred years old. Since its discovery by Pascal and Fermat in the seventeenth century it has become an integral part of our everyday lives. At one time or another all of us have made decisions by taking chances, throwing dice, or drawing cards. Frequently we have made judgments based on the likelihood or probability that a certain event will happen. Developments in the theory and applications of probability range from simple informal activities to important fields as the physical sciences, genetics, the social sciences, economics, industry, engineering and insurance. Because of its widespread use, the theory of probability should be presented in high school mathematics classes.
In this unit of curriculum we will try to improve the students’ understanding of the elementary ideas included in probability theory. The unit will clearly define important words and ideas. Formulas for solving problems will be presented. Permutations, combinations, and compound probability will be discussed. Applications of the theory to practical problems will be demonstrated in the unit. Following the explanation of each topic a set of practice exercises will be given. There are several basic objectives for this unit of study. Upon completion of the unit, the student will be able to:
understand and appreciate the use of probability in everyday life.
solve problems involving permutations and combinations.
define basic terms used in mathematical probability.
compute the probability that a certain event will happen.
The material developed here may be taught as a complete unit in algebra 3 classes, or parts of it may be extracted and taught at the following levels of instruction: (1) in seventh or eighth grade mathematics classes; (2) in high school applied mathematics classes; (3) in first year algebra or second year algebra classes; (4) in adult basic education classes.