BUS 31.4 Chapter 2 - Copy

# BUS 31.4 Chapter 2 - Copy - Chapter 2 Probability S...

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Chapter 2 – Probability S. Neuburger Review of Probability The future is uncertain. Probability measures the uncertainty of alternative outcomes. 0 ≤ P(event) ≤ 1 P(A)=0 when A will never occur P(A)=1 when A will always occur All possible outcomes together have probability 1 The probability that an event does not occur is 1-P(event) Sets - Venn Diagrams for sample space Mutually Exclusive events – only one of them can occur in a given trial Collectively Exhaustive events – includes every possible outcome Law of Addition: P(A or B) = P(A) + P(B) – P(A and B) Independent vs. Dependent events Does the occurrence of one event have any effect on the likelihood of the occurrence of the second? Independent events: Marginal (simple), join, and conditional probabilities are easy to compute P(AB) = P(A) P(B) P(A|B) = P(A) Dependent Events: P(A|B) = P(AB) / P(B) So P(AB) = P(A|B) P(B) Bayes’ Theorem – Posterior probabilities ) ( ) | ( ) ( ) | ( ) ( ) | ( ) | ( A P A B P

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BUS 31.4 Chapter 2 - Copy - Chapter 2 Probability S...

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