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Topic_probability - Chapter 5 Probability Fall 2008 1...

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Chapter 5 Probability Fall 2008 1
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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 long-term behavior of experiments Fall 2008 2
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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
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Probability Understanding Rules of Probability Probability relates short-term results to long- term results An example: A short-term result: We can obtain 0, 1, 2, or 3 heads when flipping a coin 3 times A long-term result: A “fair” coin would yield heads 1/2 of the time – we would like to use this theory in modeling Fall 2008 4
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Probability Understanding Rules of Probability Relation between long-term 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
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Probability Terms and Definitions Some definitions An experiment is a repeatable process where the results are uncertain An 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
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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 An will use capital letters such as Outcomes are also sometimes called … we will use lower case letters such as for outcomes / simple events Example (continued) One of the events … E = {roll an even number} Fall 2008 7
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Probability Understanding Rules of Probability If E is an event, then we write P ( E ) as the probability of the event E happening Probability Rules: The probability of any event must be greater than or equal to 0 and less than or equal to 1 The sum of the probabilities of all outcomes in the sample space must equal 1 Note: probabilities can be written as decimals (0, 0.3, 1.0), or as percents (0%, 30%, 100%), or as fractions (3/10) Fall 2008 8
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Probability Understanding Rules of Probability
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