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Chapter 7 Probability Fundamental Statistics for the Behavioral Sciences, 5th edition David C. Howell © 2003 Brooks/Cole Publishing Company/ITP

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2Chapter 7 Probability Major Points Probability definedProbability defined Basic terminologyBasic terminology Laws of probabilityLaws of probability Discrete variablesDiscrete variables Continuous variablesContinuous variables Cont.

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3Chapter 7 Probability Major Points --cont. An exampleAn example Review questionsReview questions

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4Chapter 7 Probability Probability Defined Analytic viewAnalytic view Relative frequency viewRelative frequency view Subjective probability viewSubjective probability view

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5Chapter 7 Probability Basic Terminology Sample with replacementSample with replacement Sample without replacementSample without replacement EventsEvents XIndependent events XMutually exclusive events XExhaustive outcomes

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6Chapter 7 Probability More Terminology Joint probabilityJoint probability XThe probability of the co-occurrence of two or more events Conditional probabilityConditional probability XThe probability of the occurrence of one event given that some other event has occurred

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7Chapter 7 Probability Laws of Probability The additive lawThe additive law XGiven a set of mutually exclusive events, the probability of the occurrence of one event or another is equal to the sum of their separate probabilities. The multiplicative lawThe multiplicative law XThe probability of the joint occurrence of two or more independent events is the product of their individual probabilities.

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8Chapter 7 Probability Discrete Variables A discrete variable is one that can take on only a limited number of possible values.A discrete variable is one that can take on only a limited number of possible values. Events are clearly classed as falling into one or another category or value.Events are clearly classed as falling into one or another category or value. We can talk about the probability of a specific outcomeWe can talk about the probability of a specific outcome

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9Chapter 7 Probability Continuous Variables There are a limitless number of possible values for this variableThere are a limitless number of possible values for this variable The probability distribution is continuous, and we speak about the probability of falling in an interval, but not the probability of a specific outcomeThe probability distribution is continuous, and we speak about the probability of falling in an interval, but not the probability of a specific outcome The ordinate of the distribution is labeled densityThe ordinate of the distribution is labeled density

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10Chapter 7 Probability An Example The Associated Press reported on a study linking radioactivity to cancer deaths among nuclear workers.The Associated Press reported on a study linking radioactivity to cancer deaths among nuclear workers. X29% of all deaths among former workers at a nuclear site were due to cancer. But...But... X35% of deaths in general population aged 44-65 are attributable to cancer Xhttp://www.stats.org/ http://www.stats.org/ Search for radioactivity and select 1997 dubious awards.Search for radioactivity and select 1997 dubious awards. Cont.

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11Chapter 7 Probability Example --cont. Apply as many of the terms and concepts that have been defined above as possible to this example.Apply as many of the terms and concepts that have been defined above as possible to this example. Should nuclear workers be worried?Should nuclear workers be worried? Should non-nuclear workers be worried?Should non-nuclear workers be worried?

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12Chapter 7 Probability Review Questions What are the three different views of probability?What are the three different views of probability? What is the difference between mutually exclusive and exhaustive?What is the difference between mutually exclusive and exhaustive? When would you use the additive law, and when the multiplicative law?When would you use the additive law, and when the multiplicative law? Give an example of a joint probability.Give an example of a joint probability. Cont.

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13Chapter 7 Probability Review Questions -- cont. Give an example of a conditional probability.Give an example of a conditional probability. Why do we use density rather than probability on the ordinate with a continuous variable?Why do we use density rather than probability on the ordinate with a continuous variable? How might we tell if two events are independent?How might we tell if two events are independent?

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