FIRST PRINCIPLES
Amy S Wagaman, Robert P. Dobrow · 2021
Probability begins with some activity, process, or experiment whose outcome is uncertain. There are definite limitations to constructing a rigorous mathematical theory out of the intuitive and empirical view of probability. One of the most basic, and important, properties of a probability function is the simple addition rule for mutually exclusive events. The simplest probability model for a finite sample space is that all outcomes are equally likely. Computing probabilities for equally likely outcomes takes a fairly simple form. Using random numbers on a computer to simulate probabilities is called the Monte Carlo method. Monte Carlo tools are used extensively in statistics, physics, engineering, and across many disciplines. The Monte Carlo simulation approach is based on the relative frequency model for probabilities. The chapter ends with problem-solving strategies and a first look at simulation.