Appendix B: The Essentials of Probability
In this section, we give a brief review of the basic probability concepts and definitions used or alluded to in this book. For further information, there are many excellent books on probability (e.g., see the book by Ross, 2002).
The space of all possible outcomes of an experiment is labeled Ω. Events are subsets of the space of all possible outcomes, A ⊂ Ω. Given two events A, B, the event
The probability of an event A is written as P(A) or Prob(A). It must be true that for any event A, 0 ≤ P(A) ≤ 1. In addition,
Given two events A, B with P(B) > 0, the conditional probability of A given the event B has occurred, is defined by
Two events are therefore independent if and only if P(A | B) = P(A) so that the knowledge ...