<< Chapter < Page Chapter >> Page >
Early developments of probability as a mathematical discipline came as a response to questions about games of chance played repeatedly. The mathematical formulation owes much to the work of Pierre de Fermat and Blaise Pascal in the seventeenth century. The game is described in terms of a well defined trial (a play); the result of any trial is one of a specific set of distinguishable outcomes. Although the result of any play is not predictable, certain “statistical regularities” of results are observed. In classical probability, the possible results are described in ways that make each result seem equally likely. If there are N such possible “equally likely” results, each is assigned a probability 1/N.The developers of mathematical probability also took cues from early work on the analysis of statistical data. To apply these results, one considers the selection of a member of the population on a chance basis. One then assigns the probability that such a person will have a given condition. The trial here is the selection of a person, but the interest is in the condition. Out of this statistical formulation came an interest not only in probabilities as fractions or relative frequencies but also in averages or expectatons. These averages play an essential role in modern probability. This approach avoided the "equally likely" limitation of classical probability.Inherent in informal thought, as well as in precise analysis, is the notion of an event to which a probability may be assigned as a measure of the likelihood the event will occur will occur on any trial. A successful mathematical model must formulate these notions with precision. The event corresponding to some characteristic of the possible outcomes is the set of those outcomes having this characteristic. The event occurs if and only if the outcome of the trial is a member of that set (i.e., has the characteristic determining the event).

Introduction

Probability models and techniques permeate many important areas of modern life. A variety of types of random processes, reliability models andtechniques, and statistical considerations in experimental work play a significant role in engineering and the physical sciences. The solutions of managementdecision problems use as aids decision analysis, waiting line theory, inventory theory, time series, cost analysis under uncertainty — all rooted inapplied probability theory. Methods of statistical analysis employ probability analysis as an underlying discipline.

Modern probability developments are increasingly sophisticated mathematically. To utilize these, the practitioner needs a sound conceptual basis which, fortunately,can be attained at a moderate level of mathematical sophistication. There is need to develop a feel for the structure of the underlying mathematical model, for the roleof various types of assumptions, and for the principal strategies of problem formulation and solution.

Probability has roots that extend far back into antiquity. The notion of “chance” played a central role in the ubiquitous practice of gambling. Butchance acts were often related to magic or religion. For example, there are numerous instances in the Hebrew Bible in which decisions were made“by lot” or some other chance mechanism, with the understanding that the outcome was determined by the will of God. In the New Testament, thebook of Acts describes the selection of a successor to Judas Iscariot as one of “the Twelve.” Two names, Joseph Barsabbas and Matthias, wereput forward. The group prayed, then drew lots, which fell on Matthias.

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Applied probability' conversation and receive update notifications?

Ask