pp.67-88 - 67 Probability Probability is a numerical...

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Probability Probability is a numerical measure of the chance, or likelihood, that something will happen. Some basic definitions…. Experiment —a process that generates well- defined outcomes. However, which of the outcomes will be realized is not known prior to conducting the experiment. Examples : Toss a coin. I will either get heads or tails. Toss a die: I will either get 1,2,3,4,5, or 6. Take an exam: I will either get 0,1,2,…,100 Fly from New York to Charlotte: It will take somewhere between 80 and 95 minutes 67 0 0.5 1.0 Increasing Likelihood of Occurrence
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Sample Space —The sample space for an experiment is the set of all experimental outcomes. Example: For the die tossing experiment, the sample space is {1,2,3,4,5,6} An element of the sample space is called a sample point . For example, the “3” is a sample point for the die tossing experiment. Assigning Probabilities: 1. The probability assigned to each experimental outcome must be between 0 and 1 inclusive. Formally, i 0 P(E ) 1.0 2. The sum of the probabilities for all the experimental outcomes equals 1.0 1 2 n P(E )+P(E ). ....+P(E )=1.0 How do we assign probabilities? There are three basic approaches: Classical, Relative Frequency, and Subjective. 68
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Classical Method : This method is only appropriate when each experimental outcome is equally likely. Thus, the classical method would work for coin tossing, or dice tossing, or most games of chance. If there are n experimental outcomes, the probability of one of them occurring is 1/n . Examples: What’s the probability of getting a 5 on a single toss of a die? What’s the probability of drawing the King of Diamonds from a deck of cards? Relative Frequency Method : Appropriate when a large number of data (observations) are available for estimating probability. Example : A random sample of 300 college students revealed that 120 exercised for 30 minutes or more at least 5 times per week. The probability that a randomly selected college student exercises for 30 minutes or more at least five times per week is: 120/300 = 0.40. For 1200 dorm room insurance policies sold, 36 resulted in theft claims. The (relative frequency) probability that a theft claim will 69
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36/1200 = 0.03 Subjective Method : A subjective probability is the measure of a person’s degree of belief that an event will happen. This is a reasonable method to use when events are not equally likely and a large amount of data is not available for constructing relative frequency probabilities. Examples : The probability that USC will beat Georgia in their next football game is: The probability that you will get an 80 or higher on your next statistics exam is: The probability that a national healthcare policy passes is: No matter which definition of probability is used, probability must obey the rules! i
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pp.67-88 - 67 Probability Probability is a numerical...

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