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Chapter 8

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

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Chapter 8

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  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 probabilityis 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: • Probabilities must be positive and between 0 and 1 0  P(E)  1 • The sum of all probabilities of all possible events must add up to 1 P(E1) + P(E2) + ... + P(En) = 1 • Probabilities are aditive P(E1 or E2) = P(E1) + P(E2)

  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 E1 E2

  6. $100 .40 .60 $10 $100 .40 .60 $10 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.

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