Probability: An Introduction with Statistical Applications, 2nd Edition

Chapter 1Sample Spaces and Probability

1.1 Discrete Sample Spaces

Probability theory deals with situations in which there is an element of randomness or chance. Some models of the physical world are deterministic, that is, they predict exactly what will happen under certain circumstances. For example, if an object is dropped from a height and given no initial velocity, its distance, , from the starting point is given by , where is the acceleration due to gravity and is the time. If one tried to apply the formula in a practical situation, one would not find very satisfactory results. The problem is that the formula applies only in a vacuum and ignores the shape of the object and the resistance of the air as well as other factors. Although some of these factors can be determined, we generally combine them and say that the result has a random or chance component. Our model then becomes , where denotes the random component of the model. In contrast with the deterministic model, this model ...