5. Chapter 10.pptx - Chapter 10 General Rules of...

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Chapter 10 General Rules of Probability Chapters objectives Independent events Conditional probability Multiplication rule Tree diagrams Baye’s Theorem
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Recall in Chapter 9 we introduced terminology and notation around defining the probability of events. Sample Space, S= set of all possible outcomes from which we define events of interest. In addition we spoke about the idea of the: Union of events: Where represents the intersection between events A and B. We also discussed how events are Mutually Exclusive (disjoint) if
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Intersection of Events and Independence Independence is a statistical (Mathematical) concept. We say that two events are independent (not associated) if they do not influence each other. Hence knowing the outcome of one event does not help with knowing the outcome of the other event.
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Definition : Two events, A and B, are independent If and only if (IFF) This definition also works the other way round: IF THEN A and B are independent If events are not independent then we say that they are dependent.
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What is the probability of being stressed and having low income? Income Low Mediu m High Tota l Stressed 526 274 216 101 6 Not stressed 1954 1680 1899 553 3 Total 2480 1954 2115 654 9
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Example: Is being stressed independent of having a Low Income? a) Yes b) No c) Not enough Information provided Income Low Mediu m High Tota l Stressed 526 274 216 101 6 Not stressed 1954 1680 1899 553 3 Total 2480 1954 2115 654 9
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ANS…
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Independence of Complements: If events A and B are independent then…
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Summary Independence vs. ME Independence ME Pr(AB)=Pr(A)Pr(B) Pr(AB)=0
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Conditional Probability
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