Mathematical Models for Society and Biology, 2nd Edition

Appendix D

Conditional Probability

A few facts concerning conditional probability needed in Chapter 3 are reviewed here. For further details, consult Chapters 6 and 7 of the book by Ross [99].

Let A and B denote events in a sample space S. The conditional probability of A given B, written prob(A|B), is defined by

(D.1)

where AB is the joint event of A and B. When prob(A|B) = prob(A), we say that A and B are independent.

As an example, suppose that X and Y are discrete random variables taking on non-negative integer values. If A is the event “X = k” and B is “Y = i,” then (D.1) becomes

Let B_i be a collection of disjoint events indexed by i whose ...