TABLE OF CONTENTS We assume that the reader has had some exposure to the basic principles of probability. In the first section of Chapter 14, a brief review of that topic was given to establish the concepts and notation relevant to our treatment of the space navigation problem. In this appendix we provide a more detailed account of probability theory [ ] for those readers whose background in this fundamental subject may be somewhat skimpy.
Consider an experiment whose outcome depends upon chance tossing a coin, rolling a pair of dice, drawing a card from a bridge deck, or sampling a population. Basic to any analysis is the set of elements consisting of all possible distinct outcomes of the experiment. We call this set the sample space for the experiment, using the term space as a synonym for the word set in this connection. The individual elements or points of the sample space are often called sample points.
Let S represent the sample space (for example, the 52 cards in a deck) and assume that the experiment in question (drawing a single card) is performed a large number of times N. Then for any event A (such as obtaining the ace of spades) let n A be the number of occurrences of A in the N trials and define
Clearly, 0 ? n A ? N, so that 0 ? p A ? 1. Furthermore, let us assume that
