1. Chapter 8 An Introduction to Probability Guillermo Gutierrez-Alcaraz

2. Probability is simply the likelihood of an event occurring, is the expression of man´s ignorance. There are two types of probability: –Objective probability is based on a frequentist or trials point of view. –Subjective probability is based on data, knowledge, experience, and beliefs about the subject being discussed.

3. Probability is base on three axioms that must be followed to ensure correct application: 1.Probabilities must be positive and between 0 and 1 0  P(E)  1 2.The sum of all probabilities of all possible events must add up to 1 P(E 1 ) + P(E 2 ) +... + P(E n ) = 1 3.Probabilities are aditive P(E 1 or E 2 ) = P(E 1 ) + P(E 2 )

4. Mutually exclusive. If one event occurs then none of the other event can occur. Collectively exhaustive. Event 1 or Event 2 or both Events must occur.

5. Venn Diagrams provide a graphical representation of probability and are often useful in defining events E1E1 E2E2

6. $100 $10 $100 $10.40.60.40.60 Probability tree example

7. Summary Probability provides the ability to express our state of knowledge in a qualitative manner. Incorporate uncertainties into the analysis. An analysis without probability can only be deterministic.