lecture notes-Chapter3.3-3.5

lecture notes-Chapter3.3-3.5 - Chapter 3.3 Probability...

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Chapter 3.3 Probability Equiprobable model: If there are n equally likely possibilities, of which one much occur and s are regarded as favorable, or as a “success,” then the probability of a “success” is given by . n s Example: When we roll a pair of fair dice, what is the probability of getting a 7? Frequency model: The probability of an event (or outcome) is the proportion of times the event would occur in a long run of repeated experiments. Personal or subjective evaluations 3.4 Axioms of Probability Probabilities are values of additive set functions. Axioms of Probability 1. For each event A in S , . 1 ) ( 0 A P 2. . 1 ) ( = S P 3. If A and B are mutually exclusive events in S , then ). ( ) ( ) ( B P A P B A P + = 3.5 SOME ELEMENTARY THEOREMS Theorem 3.4 If n A A A , , 2 1 are mutually exclusive events in a sample space S , then ). ( ) ( ) ( ) ( 2 1 2 1 n n A
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Unformatted text preview: A P A P A A A P + + + = ∪ ∪ ∪ Theorem 3.5 If A is an event in the finite sample space S , then P( A ) equals the sum of the probabilities of the individual outcomes comprising A . Theorem 3.6 (Generalized addition rule) If A and B are any events in S , then ). ( ) ( ) ( ) ( B A P B P A P B A P ∩-+ = ∪ Theorem 3.7 (Complement rule) If A is any event in S , then ). ( 1 ) ( A P A P c-= EXAMPLE: The probability that an integrated circuit chip will have defective etching is 0.2, the probability that it will have a crack defect is 0.3, and the probability that it has both defects is 0.1. What is the probability that a newly manufactured chip will have either an etching or a crack defect? (See problem 3.46)...
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  • Fall '03
  • Mendell
  • Probability, Probability theory, mutually exclusive events, Probability Equiprobable model

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