1 Probability Lite

# 1 Probability Lite - Dr Harvey A Singer School of...

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© 2007 by Harvey A. Singer 1 OM 210:  Statistical Analysis for  Management Basic Probability Part 1: Possibilities and Probabilities Dr. Harvey A. Singer School of Management George Mason University

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© 2007 by Harvey A. Singer 2 Topics List and Organization Possibilities. Basic terminology. Visualizing possibilities. Counting rules. Probability. Define probability. Assigning probabilities. Some basic rules. Displaying probabilities. Working with probability.
© 2007 by Harvey A. Singer 3 Basic Terminology A random experiment or trial is any random process or situation that results in well-defined outcomes whose occurrences are uncertain. The simplest, most fundamental, possible results from any random experiment are called the basic possible outcomes or simply outcomes . Occasionally, outcomes may also be referred to as sample points. An event is a collection of related outcomes. Related outcomes are aggregated into events. The sample space for a random experiment is the set of all possible outcomes. A sample space is collectively exhaustive. A sample space with a countable number of outcomes is discrete .

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© 2007 by Harvey A. Singer 4 Basic Terminology Outcomes (events) are mutually exclusive of each other if and only if one outcome (event) can result from any single trial of the experiment. Applies to outcomes of a single trial. For two mutually exclusive events, either one may occur but both cannot occur together (i.e., at the same time). Two events are independent of each other if and only if the occurrence of one event is in no way affected by the occurrence or non- occurrence of the other. Applies to successive trials.
© 2007 by Harvey A. Singer 5 Remarks about Independence Event occurrence or non-occurrence does NOT affect the probability of some other event. E.g., toss a fair coin twice. Causality is not implied. Really addresses the process more than the events themselves. For a coin, the outcomes of heads and tails are mutually exclusive. Any single toss is independent of any other toss. No history: no past and no future. No memory of the history of the process. Suited for “games of chance.”

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© 2007 by Harvey A. Singer 6 Mutually Exclusive vs. Independence These are two separate concepts. One does not imply the other. Two questions: Of two events, can only one event occur at a time? • If yes, then the events can’t occur together. – They are mutually exclusive. » As in games of chance. • If no, then in addition to any one of them occurring individually, both of them may occur together. They are not mutually exclusive and can occur jointly. » Real world of business, finance, and economics.
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1 Probability Lite - Dr Harvey A Singer School of...

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