Chapter 7 - Making Hard Decisions R. T. Clemen, T. Reilly...

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Unformatted text preview: Making Hard Decisions R. T. Clemen, T. Reilly Chapter 7 Probability Basics Lecture Notes by: J.R. van Dorp and T.A. Mazzuchi http://www.seas.gwu.edu/~dorpjr/ Slide 1 of 62 COPYRIGHT 2006 by GWU Draft: Version 1 Probability Basics Chapter 7 aking Hard ecisions R. T. Clemen, T. Reilly Making Hard Decisions R. T. Clemen, T. Reilly Chapter 7 Probability Basics Lecture Notes by: J.R. van Dorp and T.A. Mazzuchi http://www.seas.gwu.edu/~dorpjr/ Slide 2 of 62 COPYRIGHT 2006 by GWU Draft: Version 1 Introduction Let be an event with possible outcomes: A 1 , , n A A " A = Flipping a coin 1 A = 2 A = {Heads} {Tails} The total event (or sample space) of event is the collection of all possible outcomes of A A = {Heads, Tails} Formally: 1 2 1 1 n n n i i A A A A A = = = " Making Hard Decisions R. T. Clemen, T. Reilly Chapter 7 Probability Basics Lecture Notes by: J.R. van Dorp and T.A. Mazzuchi http://www.seas.gwu.edu/~dorpjr/ Slide 3 of 62 COPYRIGHT 2006 by GWU Draft: Version 1 Probability Calculus Probability rules may be derived using VENN DIAGRAMS 1. Probabilities must be between 0 and 1 for all possible outcomes in the sample space : 1 A P r ( ) 1 , i A for all outcomes that are in i A Ratio of the area of the oval and the area of the total rectangle can be interpreted as the probability of the event Making Hard Decisions R. T. Clemen, T. Reilly Chapter 7 Probability Basics Lecture Notes by: J.R. van Dorp and T.A. Mazzuchi http://www.seas.gwu.edu/~dorpjr/ Slide 4 of 62 COPYRIGHT 2006 by GWU Draft: Version 1 Probability Calculus 2. Probabilities must add up if both events cannot occur at the same time : 1 A 2 A ) Pr( ) Pr( ) Pr( 2 1 2 1 2 1 A A A A A A + = = Making Hard Decisions R. T. Clemen, T. Reilly Chapter 7 Probability Basics Lecture Notes by: J.R. van Dorp and T.A. Mazzuchi http://www.seas.gwu.edu/~dorpjr/ Slide 5 of 62 COPYRIGHT 2006 by GWU Draft: Version 1 Probability Calculus 3. If are all the possible outcomes and not two of these can occur at the same time , their Total Probability must sum up to 1: 1 , , n A A " 1 A 2 A 3 A 1 , , n A A " are said to be collectively exhaustive and mutually exclusive Making Hard Decisions R. T. Clemen, T. Reilly Chapter 7 Probability Basics Lecture Notes by: J.R. van Dorp and T.A. Mazzuchi http://www.seas.gwu.edu/~dorpjr/ Slide 6 of 62 COPYRIGHT 2006 by GWU Draft: Version 1 Probability Calculus 4. The probability of the complement of equals 1 minus the probability of 1 A 1 A 1 A 1 A ) Pr( 1 ) Pr( 1 1 A A = Making Hard Decisions R. T. Clemen, T. Reilly Chapter 7 Probability Basics Lecture Notes by: J.R. van Dorp and T.A. Mazzuchi http://www.seas.gwu.edu/~dorpjr/ Slide 7 of 62 COPYRIGHT 2006 by GWU Draft: Version 1 Probability Calculus 5. If two events can occur at the same time the probability of either of them happening or both equals the sum of their individual probability...
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This note was uploaded on 01/26/2010 for the course ADMS 3300 taught by Professor Shamimabdullah during the Spring '10 term at York University.

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Chapter 7 - Making Hard Decisions R. T. Clemen, T. Reilly...

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