Concepts from probability and statistics appear in a wide variety of applications in everyday life. All of us have heard reports on the chance of rain from a weather forecaster, odds on a football or basketball game, or chances of surviving life threatening diseases. There are a variety of reasons for using probability and statistics to try to understand the behavior of social and scientific phenomena. One reason is that the underlying process is far too complicated to understand as in the examples above. Using probability theory and statistics will at least give some qualitative and approximate quantitative information about the phenomena. For example, the weather that we are experiencing today is due to physical processes that have occurred over the recent past. You can see this on most weather forecasts where a satellite view of the cloud patterns is shown during the weather forecast. The problem is that identifying all the factors and relationships necessary to determine the influence weather patterns is next to impossible. Although researchers have made a good deal of progress on local weather prediction, currently there is no feasible way of predicting global weather patterns.
Another important place where probability and statistics is used is in the case when it is only necessary to have an estimate of some quantity such as the total annual precipitation in some region. If decisions must be made based on the average value of some measurable quantity the concepts from probability and statistics can be used to find appropriate qualitative information about a given process.
The use of statistical modeling to approximately answer practical questions where mathematical models are either too complicated or not known is increasing. In order to have any hope of understanding how to apply statistical modeling to complicated problems we should start with a very simple problem to frame the process of developing a statistical model. One of the simpler problems of this type is the Gambler's Ruin problem which has been studied in some detail. In the next section we will discuss this problem.