It originated as a rigorous discipline when mathematicians of the 17th century began calculating the odds in various games of chance. Probability theory is now a major branch of mathematics with widespread applications in science and engineering. Statistics is the mathematical science of utilizing data about a population in order to describe it usefully and to draw conclusions and make decisions. The population may be a community, an organization, a production line, a service counter, or a phenomenon such as the weather.
Statisticians develop models based on probability theory.
They determine which probability model is correct for a given type of problem and they decide what kinds of data should be collected and examined. This often calls for use of techniques of computer-based data analysis. Operations research is a discipline dealing with various problems in which optimization must be achieved in some sense, such as allocation of resources with optimization relative to yield for fixed cost, time, manpower, etc. Such problems arise, for example, in connection with management science, hospital administration, and urban planning. The tools used in operations research include probability theory and statistics.