Probability Tools and Techniques

The theory of probability is a mathematical theory to analyze experiments with multiple outcomes where one does not know a priori which outcome will actually occur. Such experiments are usually called random experiments. A natural and accepted way to model such phenomena is to associate a number called probability to each possible outcome. These numbers are supposed to reflect the chances of occurrence of the different outcomes. How these numbers are arrived at (more specifically, the numerical value of these probabilities) is not the major concern in developing a mathematical model. It must however be noted that in practical applications of probability models, these numerical values would matter in determining how close the model is to reality. Before we go to the axiomatic definition of probability, here are a few simple and familiar examples.