ABSTRACT
This chapter provides an illustration of a famous conditional probability problem. Generally one’s beliefs about uncertain events can change when new information is obtained. Conditional probability provides a way to precisely say how one’s beliefs change. One of the most popular casino games is craps. The chapter describes a basic version of the game and uses the multiplication rule together with the use of conditional probabilities to find the probability of winnings. Probabilities are conditional in that one’s opinion about an event is dependent on current state of knowledge. Bayes' rule provides a mechanism for changing probabilities when new data is obtained. The chapter describes the computation of an inverse probability using a tree diagram and a Bayes' box.
