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chapter11 - 11.1 Theories of Probability There are Two...

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Unformatted text preview: 11.1 Theories of Probability There are Two Basic Assumptions of the Classical Theory (P(A)=f/n): 1) All possible outcomes are taken into account. 2) All possible outcomes are equally probable. 11.1 Continued The Relative Frequency Theory: P(A)=f/n Computations are dependent upon the observed frequency of events. 11.1 Continued The Classical Method and the Relative Frequency Method Only Assign Probabilities to Classes of Events. 11.1 Continued The Subjectivist Theory: Probability is interpreted in terms of the beliefs of individual people. What are the odds that someone would accept on a bet? 11.2 Continued The Probability Calculus 1) The probability that an event will necessarily happen is 1. 2) The probability of an event that necessarily cannot happen is 0. 11.2 Continued The Rules of the Probability Calculus 1) Restricted conjunction rule: P(A and B) = P(A) P(B) 2) General conjunction rule: P(A and B) = P(A) P(B given A) 11.2 Continued 3) Restricted disjunction rule: P(A or B) = P(A) + P(B) 4) General disjunction rule: P(A or B) = P(A) + P(B) P(A and B) 5) Negation rule: P(A) = 1 P(not-A) 11.2 Continued 6) Bayes's Theorem: P(A1 given B) = P(A1) P(B given A1) [P(A1) P(B given A1)] + [P(A2) P(B given A2)] 11.2 Continued Additional Applications ...
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