The Rules of Probability
5.1 Combinations of Events
It has been shown how your uncertainty of an event E, when you know or suppose event F to be true, can be described by a number , termed your probability of E, given F. This is for a knowledge base that will be supposed fixed throughout the following discussion and therefore mostly omitted from the notation. In almost all practical cases, several uncertainties, or probabilities, are involved and it is necessary to combine them to reach an overall measure. Probabilities combine according to rules, and the aim of this chapter is to explain the rules so that you can perform the necessary calculations. There are three basic rules from which all others can be derived; one of them is slight and the other two are developed from the two ways in which events may be combined. This chapter begins with a study of these two ways.
We have already seen in §4.2 one way in which two events can be combined. If E and F are any two events, then the event that is true if, and only if, both events are true, was written E & F, or more succinctly, EF. It is called the conjunction of the two events. If E is the event of rain tomorrow, Saturday, and F is the event of rain on Sunday, then EF is the event that it rains on both days. If E is the event that a person is white, and F is the event that the same person is male, then EF is the event that ...