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Unformatted text preview: Chapter 5 Probability Fall 2008 1 Chapter 5 Preview ● When we talk about probability , we are talking about a (mathematical) measure of how likely it is for some particular event to happen ● Probability deals with chance behavior We study outcomes , or results of experiments Each time we conduct an experiment, we may get a different result Probability models the longterm behavior of experiments Fall 2008 2 Chapter 5 Preview ● Descriptive statistics, describing and summarizing data, deals with data as it is ● Probability , modeling data, deals with data as it is predicted to be ● The combination of the two will let us do our inferential statistics techniques in future chapters Fall 2008 3 Probability Understanding Rules of Probability ● Probability relates shortterm results to long term results ● An example: A shortterm result: We can obtain 0, 1, 2, or 3 heads when flipping a coin 3 times A longterm result: A “fair” coin would yield heads 1/2 of the time – we would like to use this theory in modeling Fall 2008 4 Probability Understanding Rules of Probability ● Relation between longterm and theory: The long term proportion of heads after a great many flips is 1/2 This is called the Law of Large Numbers – as the number of repetitions of an experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of that outcome Helpful Hint: Look over p. 224 of your textbook for more information about the Law of Large Numbers. Fall 2008 5 Probability Terms and Definitions ● Some definitions An experiment is a repeatable process where the results are uncertain ● Some definitions An experiment is a repeatable process where the results are uncertain An outcome is one specific possible result ● Some definitions An experiment is a repeatable process where the results are uncertain An outcome is one specific possible result The set of all possible outcomes is the sample space ● Some definitions An experiment is a repeatable process where the results are uncertain An outcome is one specific possible result The set of all possible outcomes is the sample space ● Example Experiment … roll a fair 6 sided die One of the outcomes … roll a “4” The sample space … roll a “1” or “2” or “3” or “4” or “5” or “6” Fall 2008 6 Probability Terms and Definitions ● More definitions An event is a collection of possible outcomes … we will use capital letters such as E for events Outcomes are also sometimes called simple events … we will use lower case letters such as e for outcomes / simple events ● More definitions An event is a collection of possible outcomes … we will use capital letters such as E for events Outcomes are also sometimes called simple events … we will use lower case letters such as e for outcomes / simple events ● Example (continued) One of the events … E = {roll an even number} Fall 2008 7 Probability...
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