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# class03_5 - 1.017/1.010 Class 5 Combinatorial Methods for...

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1.017/1.010 Class 5 Combinatorial Methods for Deriving Probabilities Deriving Probabilities The basic idea of the conceptual/deductive approach for deriving probabilities is to break the composite experiment into parts (sub- experiments). These parts are selected so that events for each part have readily identified probabilities (e.g. they are equally likely). The rules of probability can then be used to derive the probability of complex events for the composite experiment. The approach is usually applied to problems with a finite number of discrete outcomes. The simplest application is an experiment that divides into a number of sub- experiments with independent equally likely outcomes . In this case, suppose A is the event of interest and S is the sample space. Then the probability of A is the ratio of the number of outcomes N ( A ) in A to the total number of outcomes N ( S ) : ) ( ) ( ) ( S N A N A P = Types of Experiments To evaluate numbers of outcomes and probabilities we need to distinguish different kinds of experiments: Sampling with replacement

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class03_5 - 1.017/1.010 Class 5 Combinatorial Methods for...

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