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Math 141 ch 7 part 1

Math 141 ch 7 part 1 - Probability Experiments Sample...

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Probability Experiments, Sample Spaces, and Events (II.B.1a,1c) Definition of Probability (II.B.1b,1d,2,3a) Rules of Probability (II.B.3) Counting Techniques Used in Probability (II.B.4) Conditional Probability and Independent Events (II.B.4a,4b,4c) Bayes’ Theorem (II.B.4d)
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Experiments Activities with observable results. Results are known as outcomes . Examples : a) Tossing a coin and noting the side landing uppermost. b) Rolling a six-sided die and noting the number showing uppermost. c) Choosing a piece of candy from a bowl and noting the type of candy selected.
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Sample Points, Sample Spaces and Events A sample point is an outcome of an experiment. It is an element of a set. The sample space ( S ) is the set consisting of all possible sample points of an experiment. It is a universal set . An event is a collection of sample points from an experiment. It is a subset of the sample space. An event is said to occur whenever the event contains the observed outcome.
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Types of Sample Spaces Finite Sample Spaces The experiment has a finite number of possible sample points (or outcomes). All sample points can explicitly be listed. Non-Finite Sample Spaces The experiment has an infinite number of possible sample points.
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Example : You toss a fair coin and note which side lands uppermost. a) Describe the sample space associated with this experiment. b) What are the sample points? c) What are the events?
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Mutually Exclusive Events Events that cannot occur at the same time. They do not share any common sample points. Two events, A and B , are mutually exclusive if . Example : In the previous coin example, are any non-empty events mutually exclusive?
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