## ABSTRACT

The development of the concepts of probability is both extensive and complicated. There are several definitions of probability each depending on who is defining it and the context in which it is defined. The need for subjective probability arises from an inability to always accurately answer the question of which one event will occur. Set theory is very useful in the understanding of probability theory. Measure theory has improved the reach of the theory of probability by greatly expanding the scope of events for which a probability can be computed. The probability of an event at any point in time is the conditional probability of that event given all the events preceding it have occurred. At chance nodes the decision maker averages out the probabilities on all the branches that emanate from that node and makes the decision based on the path associated with the maximum weighted average probability of the most desirable outcome.